ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...Waqas Nawaz
Waqas Nawaz Khokhar presented research on optimizing shortest path traversal and analysis for large graph clustering. The presentation outlined challenges with traditional graph clustering approaches for big real-world graphs. It proposed four optimizations: 1) a collaborative similarity measure to reduce complexity from O(n3) to O(n2logn); 2) identifying overlapping shortest path regions to avoid redundant traversals; 3) confining traversals within clusters to limit unnecessary graph regions; and 4) allowing parallel shortest path queries to reduce latency. Experimental results on real and synthetic graphs showed the approaches improved efficiency by 40% in time and an order of magnitude in space while maintaining clustering quality. Future work aims to address intermediate data explosion
Design and analysis of algorithms - Abstract ViewWaqas Nawaz
This document discusses the design and analysis of algorithms. It introduces algorithms and defines them as sets of rules to solve computational problems. It emphasizes the importance of both designing algorithms through techniques like divide-and-conquer as well as analyzing their performance through complexity analysis. The document provides examples of analyzing worst-case, best-case, and average-case runtime and uses an example algorithm to find the largest number in an array to demonstrate space and time analysis methods.
This document discusses shortest path analysis and Dijkstra's algorithm. It defines shortest path analysis as finding the minimum cumulative path between nodes on a network. Dijkstra's algorithm is described as finding the shortest paths from a starting node to all other reachable nodes. An example application calculates the shortest path from node A to G on a sample graph. The document concludes that shortest path analysis can identify key walking routes and inform improvements to pedestrian infrastructure.
The document discusses clustering techniques and provides details about the k-means clustering algorithm. It begins with an introduction to clustering and lists different clustering techniques. It then describes the k-means algorithm in detail, including how it works, the steps involved, and provides an example illustration. Finally, it discusses comments on the k-means algorithm, focusing on aspects like choosing the value of k, initializing cluster centroids, and different distance measurement methods.
This document discusses shortest path algorithms in GIS. It defines shortest path problems as finding the lowest cost path between two nodes in a graph. Topology in GIS allows accurate connectivity and contiguity analysis to run shortest path algorithms. Common shortest path problems include single-source, single-destination, and all-pairs variants. Dijkstra's algorithm is described for solving the single-source shortest path problem from a starting node to all others. Applications include finding closest facilities like hospitals and determining scenic routes between locations. An example case study finds reliable transportation routes in Houston, TX using a GIS network.
Bidirectional graph search techniques for finding shortest path in image base...Navin Kumar
The intriguing problem of solving a maze comes
under the territory of algorithms and artificial intelligence.
The maze solving using computers is quite of interest for many
researchers, hence, there had been many previous attempts to
come up with a solution which is optimum in terms of time and
space. Some of the best performing algorithms suitable for the
problem are breadth-first search, A* algorithm, best-first
search and many others which ultimately are the
enhancement of these basic algorithms. The images are
converted into graph data structures after which an algorithm
is applied eventually pointing the trace of the solution on the
maze image. This paper is an attempt to do the same by
implementing the bidirectional version of these well-known
algorithms and study their performance with the former. The
bidirectional approach is indeed capable of providing
improved results at an expense of space. The vital part of the
approach is to find the meeting point of the two bidirectional
searches which will be guaranteed to meet if there exists any
solution.
The document discusses several algorithms for finding the shortest path in a graph: Dijkstra's algorithm, Floyd-Warshall algorithm, Bellman-Ford algorithm, and genetic algorithms. It provides details on how Dijkstra's and Floyd-Warshall algorithms work, including pseudocode. Examples are given for both algorithms. Applications of the different algorithms are also discussed.
This chapter discusses clustering connections on LinkedIn based on job title to find similarities. It covers standardizing job titles, common similarity metrics like edit distance and Jaccard distance, and clustering algorithms like greedy clustering, hierarchical clustering and k-means clustering. It also discusses fetching extended profile information using OAuth authorization to access private LinkedIn data without credentials. The goal is to answer questions about connections by clustering them based on attributes like job title, company or location.
ICDE-2015 Shortest Path Traversal Optimization and Analysis for Large Graph C...Waqas Nawaz
Waqas Nawaz Khokhar presented research on optimizing shortest path traversal and analysis for large graph clustering. The presentation outlined challenges with traditional graph clustering approaches for big real-world graphs. It proposed four optimizations: 1) a collaborative similarity measure to reduce complexity from O(n3) to O(n2logn); 2) identifying overlapping shortest path regions to avoid redundant traversals; 3) confining traversals within clusters to limit unnecessary graph regions; and 4) allowing parallel shortest path queries to reduce latency. Experimental results on real and synthetic graphs showed the approaches improved efficiency by 40% in time and an order of magnitude in space while maintaining clustering quality. Future work aims to address intermediate data explosion
Design and analysis of algorithms - Abstract ViewWaqas Nawaz
This document discusses the design and analysis of algorithms. It introduces algorithms and defines them as sets of rules to solve computational problems. It emphasizes the importance of both designing algorithms through techniques like divide-and-conquer as well as analyzing their performance through complexity analysis. The document provides examples of analyzing worst-case, best-case, and average-case runtime and uses an example algorithm to find the largest number in an array to demonstrate space and time analysis methods.
This document discusses shortest path analysis and Dijkstra's algorithm. It defines shortest path analysis as finding the minimum cumulative path between nodes on a network. Dijkstra's algorithm is described as finding the shortest paths from a starting node to all other reachable nodes. An example application calculates the shortest path from node A to G on a sample graph. The document concludes that shortest path analysis can identify key walking routes and inform improvements to pedestrian infrastructure.
The document discusses clustering techniques and provides details about the k-means clustering algorithm. It begins with an introduction to clustering and lists different clustering techniques. It then describes the k-means algorithm in detail, including how it works, the steps involved, and provides an example illustration. Finally, it discusses comments on the k-means algorithm, focusing on aspects like choosing the value of k, initializing cluster centroids, and different distance measurement methods.
This document discusses shortest path algorithms in GIS. It defines shortest path problems as finding the lowest cost path between two nodes in a graph. Topology in GIS allows accurate connectivity and contiguity analysis to run shortest path algorithms. Common shortest path problems include single-source, single-destination, and all-pairs variants. Dijkstra's algorithm is described for solving the single-source shortest path problem from a starting node to all others. Applications include finding closest facilities like hospitals and determining scenic routes between locations. An example case study finds reliable transportation routes in Houston, TX using a GIS network.
Bidirectional graph search techniques for finding shortest path in image base...Navin Kumar
The intriguing problem of solving a maze comes
under the territory of algorithms and artificial intelligence.
The maze solving using computers is quite of interest for many
researchers, hence, there had been many previous attempts to
come up with a solution which is optimum in terms of time and
space. Some of the best performing algorithms suitable for the
problem are breadth-first search, A* algorithm, best-first
search and many others which ultimately are the
enhancement of these basic algorithms. The images are
converted into graph data structures after which an algorithm
is applied eventually pointing the trace of the solution on the
maze image. This paper is an attempt to do the same by
implementing the bidirectional version of these well-known
algorithms and study their performance with the former. The
bidirectional approach is indeed capable of providing
improved results at an expense of space. The vital part of the
approach is to find the meeting point of the two bidirectional
searches which will be guaranteed to meet if there exists any
solution.
The document discusses several algorithms for finding the shortest path in a graph: Dijkstra's algorithm, Floyd-Warshall algorithm, Bellman-Ford algorithm, and genetic algorithms. It provides details on how Dijkstra's and Floyd-Warshall algorithms work, including pseudocode. Examples are given for both algorithms. Applications of the different algorithms are also discussed.
This chapter discusses clustering connections on LinkedIn based on job title to find similarities. It covers standardizing job titles, common similarity metrics like edit distance and Jaccard distance, and clustering algorithms like greedy clustering, hierarchical clustering and k-means clustering. It also discusses fetching extended profile information using OAuth authorization to access private LinkedIn data without credentials. The goal is to answer questions about connections by clustering them based on attributes like job title, company or location.
The document describes best first search algorithms. It discusses how best first search algorithms work by always selecting the most promising path based on a heuristic function. The algorithm expands the node closest to the goal at each step. The document provides pseudocode for the best first search algorithm and discusses its advantages of being more efficient than breadth-first and depth-first search, but that it can also get stuck in loops like depth-first search. An example of applying best first search to a problem is given.
1) The document discusses algorithms for finding optimal bus routes between locations, including Dijkstra's algorithm and improvements made to address its limitations.
2) It analyzes shortest path algorithms based on graph theory, least transfers, and station matrices. An improved Dijkstra's algorithm is proposed to find shortest paths between any two nodes.
3) The results show the improved algorithm can determine the shortest distance and transfer routes between any four bus stations, demonstrating its accuracy and feasibility for route planning applications.
Application of Dijkstra Algorithm in Robot path planningDarling Jemima
This document discusses using Dijkstra's algorithm for robot path planning to find the shortest collision-free path between a starting and ending point. It introduces path planning and modeling the robot and obstacles. It then explains how to determine obstacles using line intersection and describes applying Dijkstra's algorithm to build a graph of nodes and find the shortest path. An example application is shown and it is concluded that Dijkstra's algorithm can effectively find the optimal path for robot navigation.
IRJET- Bidirectional Graph Search Techniques for Finding Shortest Path in Ima...IRJET Journal
This document presents a study comparing different graph search algorithms for solving mazes represented as images. The paper implements bidirectional versions of breadth-first search (BFS) and A* search and compares their performance on 8x8 and 16x16 mazes to the traditional unidirectional algorithms. For smaller 8x8 mazes, BFS performed best but for larger 16x16 mazes, bidirectional BFS was most efficient at finding the shortest path. Bidirectional search improves results but uses more space. The key aspect is finding the meeting point where the two searches meet, guaranteeing a solution if one exists.
Dijkstra's algorithm is a graph search algorithm that finds the shortest paths between nodes in a graph. It was developed by computer scientist Edsger Dijkstra in 1956. The algorithm works by assigning tentative distances to nodes in the graph and updating them until it determines the shortest path from the starting node to all other nodes. It can be used to find optimal routes between locations on a map by treating locations as nodes and distances between them as edge costs. ArcGIS Network Analysis software uses Dijkstra's algorithm to solve network problems like finding the lowest cost route, service areas, and closest facilities.
This document summarizes a paper presentation on selecting the optimal number of clusters (K) for k-means clustering. The paper proposes a new evaluation measure to automatically select K without human intuition. It reviews existing methods, analyzes factors influencing K selection, describes the proposed measure, and applies it to real datasets. The method was validated on artificial and benchmark datasets. It aims to suggest multiple K values depending on the required detail level for clustering. However, it is computationally expensive for large datasets and the data used may not reflect real complexity.
This document summarizes computational studies of two path-based traffic assignment algorithms: the disaggregate simplicial decomposition (DSD) algorithm and the gradient projection (GP) algorithm. The study used a large-scale real network in Chicago and five randomly generated networks. Results showed that the GP algorithm performed better than both versions of the DSD algorithm on all networks, finding solutions faster with fewer iterations. The GP algorithm was more efficient by maintaining a smaller set of active paths and avoiding expensive line searches through second derivative information. While DSD could find near-optimal solutions quickly, it took more time overall and maintained a larger set of paths in each iteration.
CLIQUE is an algorithm for subspace clustering of high-dimensional data. It works in two steps: (1) It partitions each dimension of the data space into intervals of equal length to form a grid, (2) It identifies dense units within this grid and finds clusters as maximal sets of connected dense units. CLIQUE efficiently discovers clusters by identifying dense units in subspaces and intersecting them to obtain candidate dense units in higher dimensions. It automatically determines relevant subspaces for clustering and scales well with large, high-dimensional datasets.
Comparison between the genetic algorithms optimization and particle swarm opt...IAEME Publication
The document compares the genetic algorithms optimization and particle swarm optimization methods for designing close range photogrammetry networks. It presents the genetic algorithm and particle swarm optimization as two popular meta-heuristic algorithms inspired by natural evolution and collective animal behavior, respectively. The document develops mathematical models representing the genetic algorithm and particle swarm optimization for close range photogrammetry network design and evaluates them in a test field to reinforce the theoretical aspects.
The document proposes a new method for efficiently finding the top-k shortest simple paths between two nodes in a graph. It precomputes shortest path trees, transforms the graph, and uses optimizations like k-reduction and adaptive thresholds to terminate path searches early. Experimental results on real and synthetic graphs show the method outperforms prior algorithms by Yen and Hershberger for discovering top-k shortest paths.
This document discusses using the Branch and Bound technique to solve the traveling salesman problem and water jug problem. Branch and Bound is a method for solving discrete and combinatorial optimization problems by breaking the problem into smaller subsets, calculating bounds on the objective function, and discarding subsets that cannot produce better solutions than the best found so far. The document provides examples of applying Branch and Bound to find the optimal path between states for the water jug problem and the shortest route between cities for the traveling salesman problem.
The solution to the single-source shortest-path tree problem in graph theory. This slide was prepared for Design and Analysis of Algorithm Lab for B.Tech CSE 2nd Year 4th Semester.
This document outlines principles of parallel algorithm design. It discusses tasks and decomposition, processes and mapping tasks to processes. Different techniques for decomposing problems are covered, including recursive, exploratory, and hybrid decomposition. Characteristics of tasks such as granularity, concurrency, and interactions are defined. Mapping techniques can help balance load and minimize communication overheads between tasks. Different parallel algorithm design models are also introduced.
The document discusses finding the shortest route from Kota Bharu to Kuala Koh National Park in Kelantan, Malaysia using Dijkstra's parallel graph algorithm. The route passes through several places including Stong Mountain, Cintawasa Mountain, and Berangkat Mountain. Dijkstra's algorithm works by assigning infinite distances at first, then updating distances through visited neighbors until reaching the destination. The shortest path found is A to C to B to D to E, representing Kota Bharu to Stong Mountain to Cintawasa Mountain to Berangkat Mountain to Kuala Koh National Park.
This document presents a scheme for interactive communication between a base station and mobile stations to efficiently allocate resources. It models the problem and analyzes an approach where the base station broadcasts a threshold and mobile stations reply to indicate if their value is above or below it. Through multiple rounds of interaction, the base station can determine the mobile station with the maximum value with significantly less overhead than non-interactive schemes. Simulation results show the proposed approach of encoding the threshold or number of users at each round performs better than baselines. Extensions consider incorporating distortion and trading off communication costs versus time.
This document outlines a method for constructing local clusters of a massive distributed graph in parallel. It does this through four main steps: (1) randomly selecting source vertices and cluster sizes, (2) computing approximate personal PageRank vectors in parallel using Pregel, (3) performing a sweep using MapReduce to produce local clusters, and (4) reconciling any cluster overlaps by assigning vertices to the lowest conductance cluster. The key contributions are algorithms for parallel approximate PageRank computation and MapReduce-based sweeping to find local clusters efficiently in distributed graphs. Experimental results demonstrate the quality of clusterings produced and the algorithm's scalability.
Lecture slides by Mustafa Jarrar at Birzeit University, Palestine.
See the course webpage at: http://jarrar-courses.blogspot.com/2012/04/aai-spring-jan-may-2012.html and http://www.jarrar.info
The lecture covers: Un-informed Search
The document describes efficient algorithms for projecting a vector onto the l1-ball (sum of absolute values being less than a threshold). It presents two methods: 1) An exact projection algorithm that runs in expected O(n) time, where n is the dimension. 2) A method for vectors with k perturbed elements outside the l1-ball, which projects in O(k log n) time. It demonstrates these algorithms outperform interior point methods on various learning tasks, providing models with high sparsity.
The document presents an approach for measuring potential parallelism in object-oriented programs by tracing dynamic dependencies, detecting parallelism via a dynamic dependence graph, and suggesting parallelization candidates, especially loops on the critical path. It does this in three main steps: 1) Tracing dynamic dependencies during program execution, 2) Identifying parallel and serial computation paths in the dynamic dependence graph, and 3) Ranking loops on the critical path by their potential for parallel speedup. An example Java program is given and its parallel execution schedule across 4 threads is shown.
Grid based method & model based clustering methodrajshreemuthiah
The document discusses several grid-based, density-based, and conceptual clustering algorithms. Grid-based approaches like STING and WAVECLUSTER cluster data by quantizing space into grids or cells. CLIQUE uses a grid-based approach to identify dense units of data. Conceptual clustering algorithms like COBWEB create hierarchical cluster trees to classify objects based on attribute probabilities.
The document discusses using the Floyd-Warshall algorithm to find the shortest paths between stoppage points in a public transportation system on a real road network. It implements the algorithm on a sample map of Pune, India, finding the shortest distances between all stoppage point pairs and then allocating vehicles to routes based on passenger needs and vehicle capacities. The results show the total distances and times required to cover the shortest paths for each allocated vehicle.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
The document describes best first search algorithms. It discusses how best first search algorithms work by always selecting the most promising path based on a heuristic function. The algorithm expands the node closest to the goal at each step. The document provides pseudocode for the best first search algorithm and discusses its advantages of being more efficient than breadth-first and depth-first search, but that it can also get stuck in loops like depth-first search. An example of applying best first search to a problem is given.
1) The document discusses algorithms for finding optimal bus routes between locations, including Dijkstra's algorithm and improvements made to address its limitations.
2) It analyzes shortest path algorithms based on graph theory, least transfers, and station matrices. An improved Dijkstra's algorithm is proposed to find shortest paths between any two nodes.
3) The results show the improved algorithm can determine the shortest distance and transfer routes between any four bus stations, demonstrating its accuracy and feasibility for route planning applications.
Application of Dijkstra Algorithm in Robot path planningDarling Jemima
This document discusses using Dijkstra's algorithm for robot path planning to find the shortest collision-free path between a starting and ending point. It introduces path planning and modeling the robot and obstacles. It then explains how to determine obstacles using line intersection and describes applying Dijkstra's algorithm to build a graph of nodes and find the shortest path. An example application is shown and it is concluded that Dijkstra's algorithm can effectively find the optimal path for robot navigation.
IRJET- Bidirectional Graph Search Techniques for Finding Shortest Path in Ima...IRJET Journal
This document presents a study comparing different graph search algorithms for solving mazes represented as images. The paper implements bidirectional versions of breadth-first search (BFS) and A* search and compares their performance on 8x8 and 16x16 mazes to the traditional unidirectional algorithms. For smaller 8x8 mazes, BFS performed best but for larger 16x16 mazes, bidirectional BFS was most efficient at finding the shortest path. Bidirectional search improves results but uses more space. The key aspect is finding the meeting point where the two searches meet, guaranteeing a solution if one exists.
Dijkstra's algorithm is a graph search algorithm that finds the shortest paths between nodes in a graph. It was developed by computer scientist Edsger Dijkstra in 1956. The algorithm works by assigning tentative distances to nodes in the graph and updating them until it determines the shortest path from the starting node to all other nodes. It can be used to find optimal routes between locations on a map by treating locations as nodes and distances between them as edge costs. ArcGIS Network Analysis software uses Dijkstra's algorithm to solve network problems like finding the lowest cost route, service areas, and closest facilities.
This document summarizes a paper presentation on selecting the optimal number of clusters (K) for k-means clustering. The paper proposes a new evaluation measure to automatically select K without human intuition. It reviews existing methods, analyzes factors influencing K selection, describes the proposed measure, and applies it to real datasets. The method was validated on artificial and benchmark datasets. It aims to suggest multiple K values depending on the required detail level for clustering. However, it is computationally expensive for large datasets and the data used may not reflect real complexity.
This document summarizes computational studies of two path-based traffic assignment algorithms: the disaggregate simplicial decomposition (DSD) algorithm and the gradient projection (GP) algorithm. The study used a large-scale real network in Chicago and five randomly generated networks. Results showed that the GP algorithm performed better than both versions of the DSD algorithm on all networks, finding solutions faster with fewer iterations. The GP algorithm was more efficient by maintaining a smaller set of active paths and avoiding expensive line searches through second derivative information. While DSD could find near-optimal solutions quickly, it took more time overall and maintained a larger set of paths in each iteration.
CLIQUE is an algorithm for subspace clustering of high-dimensional data. It works in two steps: (1) It partitions each dimension of the data space into intervals of equal length to form a grid, (2) It identifies dense units within this grid and finds clusters as maximal sets of connected dense units. CLIQUE efficiently discovers clusters by identifying dense units in subspaces and intersecting them to obtain candidate dense units in higher dimensions. It automatically determines relevant subspaces for clustering and scales well with large, high-dimensional datasets.
Comparison between the genetic algorithms optimization and particle swarm opt...IAEME Publication
The document compares the genetic algorithms optimization and particle swarm optimization methods for designing close range photogrammetry networks. It presents the genetic algorithm and particle swarm optimization as two popular meta-heuristic algorithms inspired by natural evolution and collective animal behavior, respectively. The document develops mathematical models representing the genetic algorithm and particle swarm optimization for close range photogrammetry network design and evaluates them in a test field to reinforce the theoretical aspects.
The document proposes a new method for efficiently finding the top-k shortest simple paths between two nodes in a graph. It precomputes shortest path trees, transforms the graph, and uses optimizations like k-reduction and adaptive thresholds to terminate path searches early. Experimental results on real and synthetic graphs show the method outperforms prior algorithms by Yen and Hershberger for discovering top-k shortest paths.
This document discusses using the Branch and Bound technique to solve the traveling salesman problem and water jug problem. Branch and Bound is a method for solving discrete and combinatorial optimization problems by breaking the problem into smaller subsets, calculating bounds on the objective function, and discarding subsets that cannot produce better solutions than the best found so far. The document provides examples of applying Branch and Bound to find the optimal path between states for the water jug problem and the shortest route between cities for the traveling salesman problem.
The solution to the single-source shortest-path tree problem in graph theory. This slide was prepared for Design and Analysis of Algorithm Lab for B.Tech CSE 2nd Year 4th Semester.
This document outlines principles of parallel algorithm design. It discusses tasks and decomposition, processes and mapping tasks to processes. Different techniques for decomposing problems are covered, including recursive, exploratory, and hybrid decomposition. Characteristics of tasks such as granularity, concurrency, and interactions are defined. Mapping techniques can help balance load and minimize communication overheads between tasks. Different parallel algorithm design models are also introduced.
The document discusses finding the shortest route from Kota Bharu to Kuala Koh National Park in Kelantan, Malaysia using Dijkstra's parallel graph algorithm. The route passes through several places including Stong Mountain, Cintawasa Mountain, and Berangkat Mountain. Dijkstra's algorithm works by assigning infinite distances at first, then updating distances through visited neighbors until reaching the destination. The shortest path found is A to C to B to D to E, representing Kota Bharu to Stong Mountain to Cintawasa Mountain to Berangkat Mountain to Kuala Koh National Park.
This document presents a scheme for interactive communication between a base station and mobile stations to efficiently allocate resources. It models the problem and analyzes an approach where the base station broadcasts a threshold and mobile stations reply to indicate if their value is above or below it. Through multiple rounds of interaction, the base station can determine the mobile station with the maximum value with significantly less overhead than non-interactive schemes. Simulation results show the proposed approach of encoding the threshold or number of users at each round performs better than baselines. Extensions consider incorporating distortion and trading off communication costs versus time.
This document outlines a method for constructing local clusters of a massive distributed graph in parallel. It does this through four main steps: (1) randomly selecting source vertices and cluster sizes, (2) computing approximate personal PageRank vectors in parallel using Pregel, (3) performing a sweep using MapReduce to produce local clusters, and (4) reconciling any cluster overlaps by assigning vertices to the lowest conductance cluster. The key contributions are algorithms for parallel approximate PageRank computation and MapReduce-based sweeping to find local clusters efficiently in distributed graphs. Experimental results demonstrate the quality of clusterings produced and the algorithm's scalability.
Lecture slides by Mustafa Jarrar at Birzeit University, Palestine.
See the course webpage at: http://jarrar-courses.blogspot.com/2012/04/aai-spring-jan-may-2012.html and http://www.jarrar.info
The lecture covers: Un-informed Search
The document describes efficient algorithms for projecting a vector onto the l1-ball (sum of absolute values being less than a threshold). It presents two methods: 1) An exact projection algorithm that runs in expected O(n) time, where n is the dimension. 2) A method for vectors with k perturbed elements outside the l1-ball, which projects in O(k log n) time. It demonstrates these algorithms outperform interior point methods on various learning tasks, providing models with high sparsity.
The document presents an approach for measuring potential parallelism in object-oriented programs by tracing dynamic dependencies, detecting parallelism via a dynamic dependence graph, and suggesting parallelization candidates, especially loops on the critical path. It does this in three main steps: 1) Tracing dynamic dependencies during program execution, 2) Identifying parallel and serial computation paths in the dynamic dependence graph, and 3) Ranking loops on the critical path by their potential for parallel speedup. An example Java program is given and its parallel execution schedule across 4 threads is shown.
Grid based method & model based clustering methodrajshreemuthiah
The document discusses several grid-based, density-based, and conceptual clustering algorithms. Grid-based approaches like STING and WAVECLUSTER cluster data by quantizing space into grids or cells. CLIQUE uses a grid-based approach to identify dense units of data. Conceptual clustering algorithms like COBWEB create hierarchical cluster trees to classify objects based on attribute probabilities.
The document discusses using the Floyd-Warshall algorithm to find the shortest paths between stoppage points in a public transportation system on a real road network. It implements the algorithm on a sample map of Pune, India, finding the shortest distances between all stoppage point pairs and then allocating vehicles to routes based on passenger needs and vehicle capacities. The results show the total distances and times required to cover the shortest paths for each allocated vehicle.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
The document discusses network analysis and various network problems. It defines key network terminology like nodes, arcs, directed and undirected networks. It describes common network problems like minimum spanning tree, shortest route, maximum flow, and critical path. Algorithms for solving minimum spanning tree and shortest path problems like Kruskal's algorithm and Dijkstra's algorithm are explained with examples. Applications of network analysis in areas like transportation, telecommunications, and project management are also mentioned.
This document summarizes a research article that applied dynamic programming to determine the shortest route between Umuahia and Abuja in Nigeria. It begins with an abstract that outlines using a fixed-point iterative method within a metric space to model the problem. The introduction then provides background on dynamic programming techniques like backward recursion and Dijkstra's algorithm. It also describes other algorithms like greedy and Prim's algorithm for finding minimum spanning trees. The body of the document then gives mathematical definitions and results relevant to metric spaces and fixed points. It concludes that applying this dynamic programming approach found the shortest route between the two cities to be 702 km through several connecting cities.
AN EFFECT OF USING A STORAGE MEDIUM IN DIJKSTRA ALGORITHM PERFORMANCE FOR IDE...ijcsit
The graph model is used widely for representing connected objects within a specific area. These objects are defined as nodes; where the connection is represented as arc called edges. The shortest path between two nodes is one of the most focus researchers’ attentions. Many algorithms are developed with different structured approach for reducing the shortest path cost. The most widely used algorithm is Dijkstra algorithm. This algorithm has been represented with various structural developments in order to reduce the shortest path cost. This paper highlights the idea of using a storage medium to store the solution path from Dijkstra algorithm, then, uses it to find the implicit path in an ideal time cost. The performance of Dijkstra algorithm using an appropriate data structure is improved. Our results emphasize that the searching time through the given data structure is reduced within different graphs models.
From shortest path to all-path the routing continuum theory and its applicationsNexgen Technology
Ecruitment Solutions (ECS) is one of the leading Delhi based Software Development & HR Consulting Firm, which is assessed at the level of ISO 9001:2008 standard. ECS offers an awesome project and product based solutions to many customers around the globe.
In addition, ECS has also widened its wings by the way consummating academic projects especially for the final year professional degree students in India. ECS consist of a technical team that has solved many IEEE papers and delivered world-class solutions .
From shortest path to all-path the routing continuum theory and its applicationsNexgen Technology
Ecruitment Solutions (ECS) is one of the leading Delhi based Software Development & HR Consulting Firm, which is assessed at the level of ISO 9001:2008 standard. ECS offers an awesome project and product based solutions to many customers around the globe.
In addition, ECS has also widened its wings by the way consummating academic projects especially for the final year professional degree students in India. ECS consist of a technical team that has solved many IEEE papers and delivered world-class solutions .
Jamming aware traffic allocation for multiple-path routing using portfolio se...Saad Bare
Multiple-path source routing protocols allow a data source node to distribute the total traffic among available paths. we consider the problem of jamming-aware source routing in which the source node performs traffic allocation based on empirical jamming statistics at individual network nodes. We formulate this traffic allocation as a lossy network flow optimization problem using portfolio selection theory from financial statistics. We show that in multisource networks, this centralized optimization problem can be solved using a distributed algorithm based on decomposition in network utility maximization (NUM). We demonstrate the network's ability to estimate the impact of jamming and incorporate these estimates into the traffic allocation problem. Finally, we simulate the achievable throughput using our proposed traffic allocation method in several scenarios.
A Survey on Rendezvous Based Techniques for Power Conservation in Wireless Se...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
A Survey on Rendezvous Based Techniques for Power Conservation in Wireless Se...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Improve MANET network performance using ESPS approachSurbhi Sharma
The document presents a paper on an Efficient Stable Path Selection Approach (ESPS) for improved network performance in mobile ad hoc networks. The paper proposes a new routing protocol called MCCP that uses an ant colony optimization algorithm to select the most stable path for communication between nodes. The methodology involves assumptions about the network, assigning parameters like mobility, signal strength, and node degree, and using an ACO algorithm to optimize path selection. The approach is implemented using the NS2 simulator and results show that MCCP improves performance metrics like packet delivery ratio, end-to-end delay, and throughput compared to the AOMDV routing protocol. The paper concludes that ESPS achieves more efficient and effective data transmission through stable path selection
Shortest path algorithm for data transmission in wireless ad hoc sensor networksijasuc
Wireless sensor networks determine probable in military, environments, health and commercial
applications. The process of transferring of information from a remote sensor node to other nodes in a
network holds importance for such applications. Various constraints such as limited computation, storage
and power makes the process of transferring of information routing interesting and has opened new arenas
for researchers. The fundamental problem in sensor networks states the significance and routing of
information through a real path as path length decides some basic performance parameters for sensor
networks. This paper strongly focuses on a shortest path algorithm for wireless adhoc networks. The
simulations are performed on NS2 and the results obtained discuss the role of transferring of information
through a shortest path.
The shortest not necessarily the best. other path on the basis of the optimal...eSAT Journals
The document presents an analysis of using the Dijkstra algorithm to find alternative shortest paths between nodes in a maritime traffic network. It begins by introducing the traditional method of using Dijkstra's algorithm to find the single shortest path and proposes removing edges from this path to find additional suboptimal paths. A numerical example with 29 edges between 8 islands is provided. The algorithm finds the shortest path between nodes 0 and 3, then this path is modified by removing edges to produce two additional paths. The document concludes that finding alternative paths can be done quickly using modern computers and is worth further research considering multiple criteria.
The shortest not necessarily the best other path on the basis of the optimal ...eSAT Publishing House
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(Icca 2014) shortest path analysis in social graphs
1. SHORTEST PATH
ANALYSIS IN REAL
GRAPHS
Authors
Waqas Nawaz,
Kifayat Ullah Khan,
Young-Koo Lee
Department of Computer Engineering, Kyung
Hee University, South Korea
The 3rd International Conference on Convergence
and its Application (ICCA 2014) , 25-27 June,
Seoul, Korea
2. “... shortest path problems are among the most
fundamental combinatorial optimization
problems with many applications, both direct and
as subroutines in other combinatorial optimization
algorithms. Algorithms for these problems have
been studied since the 1950’s and still
remain an active area of research.”[1]
MOTIVATION
2
[1] Camil Demetrescu, Andrew V. Goldberg, and David S. Johnson.
Implementation challenge for shortest paths. In Encyclopedia of Algorithms.
2008.
3. Telephone routes
Which communication links to activate when a user makes a
phone call, e.g. from HK to New York, USA.
Road systems design
Problem: how to determine the no. of lanes in each road?
Given: expected traffic between each pair of locations
Method: Estimate total traffic on each road link assuming each
passenger will use shortest path
Many other applications, including:
Finance (arbitrage),
In economics and finance, arbitrage is the practice of taking advantage of
a price difference between two or more markets: striking a combination of
matching deals that capitalize upon the imbalance, the profit being the
difference between the market prices. (Wikipedia)
Assembly line inspection systems design,
Graph Median, Traffic Simulation, Image Segmentation,
Drug Target Identification, Community Detection,
Social Search, Social Networking, Message Routing,
SHORTEST PATH APPLICATIONS
3
4. SHORTEST PATH ANALYSIS:
CONTRIBUTIONS
Empirically prove that a significant
amount of shortest paths are
overlapped
The behavior of the overlapped
regions in diverse networks
E.g. Scale free networks
The impact of hub-nodes on the
shortest paths
E.g. What portion of the shortest
paths are pass through the hub
nodes or across dense regions
Analysis on the coverage of the
entire graph through shortest
paths 4
Hub-nodes
5. Which portion of a graph is traversed
through shortest paths?
OR
Validate
A significant amount of shortest paths are
overlapped
Hub nodes are contained in shortest
paths
PROBLEM STATEMENT
5To the best of our knowledge, there is no such
empirical analysis exists in literature
6. DEFINITION: SHORTEST PATH (SP)
Definition: A sequence of edges i.e.
pi = Eseq = {e1 e2 … em} from source vertex vs to
destination vertex vd where dist(pi) is minimum
m is the number of edges,
ei = {(vi-1,vi, cost)|vi-1,vi Є V},
vs ≠ vd
dist(…) is the distance function based on edge cost
Example
Shortest Path = p(v0, v7) = {e1 e2 e8 e5 e6
e7 }
where m=7, vs = v0 and vd = v7
6v2 v3 v4 v5 v6 v7v1v0
e1 e2 e3
e4 e5 e6 e7
e8
e9
source destination
7. Straight Forward Approach (Brute-force)
Generate all pair shortest paths SP-DB
(file on disk)
If N is the number of vertices then N2
paths, may not appropriate for very
large graphs
Manually scan SP-DB to identify the
overlaps and frequently occurring vertices
Efficiency subjected to careful data
structure or indexing method
HOW TO ANALYZE SPS? BASIC IDEA (1/2)
7
8. Alternate Approach (Non-Exhaustive)
Generate all pair shortest paths (small
graphs) OR k-source shortest paths (for
large graphs, where k << N ) into SP-DB
Estimate the occurrences of vertices
using data mining approach
Frequent Item-set Mining with given
threshold to limit search space
We can easily prune the rarely
occurring vertices
HOW TO ANALYZE SPS? BASIC IDEA (2/2)
8
9. Shortest Path Computation
Frequent Item-set Mining towards finding SPOREs
FP-Growth approach
Each shortest path is considered as a transaction which
contains nodes as set of items
If sup = 2 then
1 len SPORE (C, D, E)
2 len SPORE (CD, DE, CE)
3 len SPORE (CDE)
NON-EXHAUSTIVE APPROACH: EXAMPLE
9
All Pair Shortest Pathsk-Source Shortest Paths, k=2
C D ENM P
C D EBA F
10. Real Dataset
Social circles from Facebook (anonymized)
Vertices (4,050), Edges (88,254), Diameter (8)
Environment
Windows 7, 32bit, Java Implementation
EXPERIMENTS
10
Original Facebook Graph Shortest Path Traversals
12. The frequency distribution of shortest
path overlaps is influenced by network
node degree distribution
The probability of the shortest path
passing through hub-nodes is high
A significant amount of shortest paths
are overlapped
CONCLUSION
12