Constraint satisfaction problems involve finding assignments of values to variables that satisfy a set of constraints. They can be represented as constraint graphs with nodes as variables and edges as constraints between variables. Problems are solved using backtracking search with heuristics like most-constrained variable selection and forward checking constraint propagation to prune the search space. More advanced techniques involve achieving different levels of consistency like arc consistency. Structured problems can leverage tree decompositions to decompose large problems. Satisfiability problems are a type of CSP that can be solved using the Davis-Putnam-Logemann-Loveland backtracking algorithm with improvements like unit propagation and learning conflict clauses.
This document defines operations research as using scientific methods and advanced analytical techniques to help make better decisions, especially regarding allocation of scarce resources. It discusses several applications of operations research including scheduling airlines and facility placement. Key operations research techniques are described like linear programming, simulation, and queuing theory. The document also defines Markov processes and Markov chains, explaining that Markov models assume the Markov property that future states only depend on the present state. It contrasts Markov chains with hidden Markov models and discusses how Monte Carlo simulation and Markov chain Monte Carlo methods are used for sampling from probability distributions.
Este documento discute as repercussões psicológicas em mulheres diagnosticadas com câncer de mama. Ele descreve como o câncer de mama é a neoplasia mais comum e mortal no sexo feminino e como o diagnóstico pode desestabilizar o equilíbrio emocional causando medo e ansiedade. O documento também discute as etapas psicológicas de negação, raiva, barganha, depressão e aceitação que as pacientes enfrentam ao lidar com o diagnóstico.
This document provides an overview of the LISP (List Processing) programming language. It discusses how LISP was commonly used for artificial intelligence programming due to its ability to modify programs dynamically. The document then describes various LISP dialects and the invention of LISP by John McCarthy. It also summarizes key LISP features like being machine-independent, providing object-oriented programming and advanced data types. The document concludes by explaining functions, predicates, conditionals, recursion, arrays, property lists, mapping functions and lambda expressions in LISP.
This document summarizes constraint satisfaction problems (CSPs). It describes CSPs as search problems where the state is defined by variables with domains of possible values, and the goal is to find assignments of values to variables that satisfy a set of constraints. It provides examples of CSPs like map coloring. It discusses representations of CSPs using constraint graphs and varieties of constraints. It also summarizes algorithms for solving CSPs like backtracking search, constraint propagation techniques, and how CSP techniques relate to solving satisfiability problems.
Constraint satisfaction problems involve finding assignments of values to variables that satisfy a given set of constraints. They can model problems like map coloring. Constraint satisfaction problems can be solved using backtracking search, which involves trying value assignments and backtracking when constraints are violated. Techniques like constraint propagation help prune the search space by detecting inconsistencies earlier. Satisfiability problems are a type of constraint satisfaction problem involving Boolean variables. Local search algorithms like GSAT provide incomplete but efficient solutions for large satisfiability instances.
The document discusses constraint satisfaction problems and constraint propagation techniques for solving such problems. It defines constraint satisfaction as solving a problem under certain constraints or rules, where the values assigned to variables must satisfy those constraints. It describes the three main components of a constraint satisfaction problem as the set of variables, their domains, and the constraints. It then discusses solving constraint satisfaction problems using techniques like backtracking search and constraint propagation methods like arc consistency and k-consistency to reduce the search space.
Constraint satisfaction problems (CSPs) define states as assignments of variables to values from their domains, with constraints specifying allowable combinations. Backtracking search assigns one variable at a time using depth-first search. Improved heuristics like most-constrained variable selection and least-constraining value choice help. Forward checking and constraint propagation techniques like arc consistency detect inconsistencies earlier than backtracking alone. Local search methods like min-conflicts hill-climbing can also solve CSPs by allowing constraint violations and minimizing them.
This document discusses constraint satisfaction problems (CSPs) and algorithms for solving them. It defines a CSP as a problem where the goal is to assign values to variables while satisfying constraints between the variables. Common examples include map coloring, scheduling problems, and the n-queens puzzle. The document outlines representations of CSPs using constraint graphs and search trees. It then describes search algorithms like backtracking with forward checking and constraint propagation using arc consistency to more efficiently prune the search space.
This document defines operations research as using scientific methods and advanced analytical techniques to help make better decisions, especially regarding allocation of scarce resources. It discusses several applications of operations research including scheduling airlines and facility placement. Key operations research techniques are described like linear programming, simulation, and queuing theory. The document also defines Markov processes and Markov chains, explaining that Markov models assume the Markov property that future states only depend on the present state. It contrasts Markov chains with hidden Markov models and discusses how Monte Carlo simulation and Markov chain Monte Carlo methods are used for sampling from probability distributions.
Este documento discute as repercussões psicológicas em mulheres diagnosticadas com câncer de mama. Ele descreve como o câncer de mama é a neoplasia mais comum e mortal no sexo feminino e como o diagnóstico pode desestabilizar o equilíbrio emocional causando medo e ansiedade. O documento também discute as etapas psicológicas de negação, raiva, barganha, depressão e aceitação que as pacientes enfrentam ao lidar com o diagnóstico.
This document provides an overview of the LISP (List Processing) programming language. It discusses how LISP was commonly used for artificial intelligence programming due to its ability to modify programs dynamically. The document then describes various LISP dialects and the invention of LISP by John McCarthy. It also summarizes key LISP features like being machine-independent, providing object-oriented programming and advanced data types. The document concludes by explaining functions, predicates, conditionals, recursion, arrays, property lists, mapping functions and lambda expressions in LISP.
This document summarizes constraint satisfaction problems (CSPs). It describes CSPs as search problems where the state is defined by variables with domains of possible values, and the goal is to find assignments of values to variables that satisfy a set of constraints. It provides examples of CSPs like map coloring. It discusses representations of CSPs using constraint graphs and varieties of constraints. It also summarizes algorithms for solving CSPs like backtracking search, constraint propagation techniques, and how CSP techniques relate to solving satisfiability problems.
Constraint satisfaction problems involve finding assignments of values to variables that satisfy a given set of constraints. They can model problems like map coloring. Constraint satisfaction problems can be solved using backtracking search, which involves trying value assignments and backtracking when constraints are violated. Techniques like constraint propagation help prune the search space by detecting inconsistencies earlier. Satisfiability problems are a type of constraint satisfaction problem involving Boolean variables. Local search algorithms like GSAT provide incomplete but efficient solutions for large satisfiability instances.
The document discusses constraint satisfaction problems and constraint propagation techniques for solving such problems. It defines constraint satisfaction as solving a problem under certain constraints or rules, where the values assigned to variables must satisfy those constraints. It describes the three main components of a constraint satisfaction problem as the set of variables, their domains, and the constraints. It then discusses solving constraint satisfaction problems using techniques like backtracking search and constraint propagation methods like arc consistency and k-consistency to reduce the search space.
Constraint satisfaction problems (CSPs) define states as assignments of variables to values from their domains, with constraints specifying allowable combinations. Backtracking search assigns one variable at a time using depth-first search. Improved heuristics like most-constrained variable selection and least-constraining value choice help. Forward checking and constraint propagation techniques like arc consistency detect inconsistencies earlier than backtracking alone. Local search methods like min-conflicts hill-climbing can also solve CSPs by allowing constraint violations and minimizing them.
This document discusses constraint satisfaction problems (CSPs) and algorithms for solving them. It defines a CSP as a problem where the goal is to assign values to variables while satisfying constraints between the variables. Common examples include map coloring, scheduling problems, and the n-queens puzzle. The document outlines representations of CSPs using constraint graphs and search trees. It then describes search algorithms like backtracking with forward checking and constraint propagation using arc consistency to more efficiently prune the search space.
This document discusses solving Sudoku puzzles using constraint satisfaction techniques. It presents the objectives, which are to examine Sudoku as a constraint satisfaction problem and determine if puzzle symmetry affects solving time. It then provides details on constraint satisfaction problems, Sudoku rules, proposed solutions using backtracking search and forward checking, evaluation of solving times for different puzzle types and analysis of results. Symmetric puzzles were found to solve faster than asymmetric ones due to providing more constraints.
The document discusses constraint satisfaction problems (CSPs). It defines a CSP as having variables with domains of possible values and constraints limiting the values variables can take. A solution assigns values to all variables while satisfying constraints. The document outlines backtracking search and constraint propagation techniques for solving CSPs, including variable and value ordering heuristics, forward checking, and arc consistency. Arc consistency is more effective than forward checking at detecting inconsistencies and pruning the search space. The document provides examples of CSP formulations for map coloring, Sudoku, and N-Queens problems.
This document discusses constraint satisfaction problems (CSP) and the CSP solving technique called forward checking. It provides an example of a map coloring CSP problem and then explains forward checking, which tracks remaining legal values for unassigned variables and terminates the search when a variable has no legal values left. It also discusses using heuristics like the degree heuristic, minimum remaining values heuristic, and least constraining value heuristic to guide the search order during forward checking.
Constraint Satisfaction Problems (CSPs) involve variables with domains of possible values and constraints specifying allowed value combinations. The document discusses CSP definitions and representations, examples like Sudoku and graph coloring, and solutions being complete consistent assignments. It also covers backtracking search for CSPs, heuristics like minimum remaining values and least constraining value, and forward checking for pruning inconsistent values earlier.
This document provides an overview of stochastic processes and Markov chains. It defines stochastic processes as families of random variables indexed by time. Markov chains are a type of stochastic process where the future state depends only on the present state, not on the past. The document discusses examples of Markov chains, transition matrices, classification of states as transient or persistent, and properties like irreducibility. It aims to introduce key concepts in stochastic processes and Markov chains.
This document discusses constraint satisfaction problems (CSPs). It defines CSPs as problems with variables that must satisfy constraints. CSPs can represent many real-world problems and are solved through constraint satisfaction methods. The document outlines CSP components like variables, domains, and constraints. It also describes representing problems as CSPs, solving CSPs through backtracking search, and the role of heuristics like minimum remaining values in improving the search process.
This document describes constraint satisfaction problems (CSPs) and techniques for solving them. CSPs model problems as variables with domains where the goal is to assign values in a way that satisfies constraints. Standard search algorithms like depth-first search can solve CSPs but are inefficient. More specialized CSP algorithms use filtering to prune values that cannot lead to solutions, enforcing consistency constraints. Variable and value ordering heuristics like minimum remaining values (MRV) and least constraining value (LCV) can significantly improve search performance. Demos illustrate CSP formulations and solving techniques.
Slides from my survey talk on Backdoors to SAT at the pre-conference workshop on New Developments in Exact Algorithms and Lower Bounds at FSTTCS 2014 in Delhi.
Effect of global market on indian marketArpit Jain
This document summarizes a study that uses Granger's causality test to analyze the impact of the Nasdaq, Hang Seng, and Nikkei stock market indices on India's Sensex index. It first provides background on time series analysis and challenges in determining stationarity and causality. It then explains key concepts like correlograms, unit roots, and random walks. The document outlines the Granger causality test methodology and reports the main results, finding causality from the Nasdaq and Nikkei to the Sensex, and from the Sensex to the Hang Seng. It concludes by noting limitations around selecting the optimal number of lags.
Bounded model checking encodes executions of a system up to a bounded length k as a propositional formula along with a property violation. If the formula is satisfiable, a counterexample is found; if unsatisfiable, no counterexample up to length k exists. The technique leverages efficient SAT solvers but is incomplete. Modern SAT solvers use conflict-driven learning and backtracking based on the Davis-Putnam-Logemann-Loveland algorithm to efficiently solve the propositional formulas generated by bounded model checking.
Avionics 738 Adaptive Filtering at Air University PAC Campus by Dr. Bilal A. Siddiqui in Spring 2018. This lecture covers background material for the course.
The Gaussian wavelet is defined as the derivative of the Gaussian probability density function. It belongs to a family of Hermitian wavelets used in continuous wavelet transforms. The nth Gaussian wavelet is the nth derivative of the Gaussian function. Gaussian wavelets have no scaling function and are not orthogonal or compactly supported, making the discrete wavelet transform and perfect reconstruction impossible. However, the continuous wavelet transform can be used to detect discontinuities in signals using Gaussian wavelets.
1. Recurrent neural networks (RNNs) allow information to persist from previous time steps through hidden states and can process input sequences of variable lengths. Common RNN architectures include LSTMs and GRUs which address the vanishing gradient problem of traditional RNNs.
2. RNNs are commonly used for natural language processing tasks like machine translation, sentiment classification, and named entity recognition. They learn distributed word representations through techniques like word2vec, GloVe, and negative sampling.
3. Machine translation models use an encoder-decoder architecture with an RNN encoder and decoder. Beam search is commonly used to find high-probability translation sequences. Performance is evaluated using metrics like BLEU score.
Elements of Inference covers the following concepts and takes off right from where we left off in the previous slide https://www.slideshare.net/GiridharChandrasekar1/statistics1-the-basics-of-statistics.
Population Vs Sample (Measures)
Probability
Random Variables
Probability Distributions
Statistical Inference – The Concept
This document proposes fast single-pass k-means clustering algorithms to allow for fast nearest neighbor search on large datasets. It discusses the rationale for using k-means clustering, describes algorithms like ball k-means and surrogate methods that can perform clustering in a single pass. It covers implementations using techniques like locality sensitive hashing and projection search to speed up vector searches. Evaluation on synthetic and real datasets shows the algorithms can achieve the same or better accuracy as traditional k-means 10x faster, enabling applications like fast nearest neighbor search on massive datasets for applications like customer modeling.
This document discusses the k-nearest neighbors (k-NN) algorithm. It begins by explaining the basic principles of k-NN, including that records close to each other in a data space will be of the same type. It then discusses issues with k-NN like computational expense, storage requirements, and performance with high-dimensional data. The document goes on to discuss techniques to improve k-NN, including condensing the training data set to reduce redundant points while retaining the decision boundary, and using proximity graphs and editing algorithms to further refine the training set.
This document discusses solving Sudoku puzzles using constraint satisfaction techniques. It presents the objectives, which are to examine Sudoku as a constraint satisfaction problem and determine if puzzle symmetry affects solving time. It then provides details on constraint satisfaction problems, Sudoku rules, proposed solutions using backtracking search and forward checking, evaluation of solving times for different puzzle types and analysis of results. Symmetric puzzles were found to solve faster than asymmetric ones due to providing more constraints.
The document discusses constraint satisfaction problems (CSPs). It defines a CSP as having variables with domains of possible values and constraints limiting the values variables can take. A solution assigns values to all variables while satisfying constraints. The document outlines backtracking search and constraint propagation techniques for solving CSPs, including variable and value ordering heuristics, forward checking, and arc consistency. Arc consistency is more effective than forward checking at detecting inconsistencies and pruning the search space. The document provides examples of CSP formulations for map coloring, Sudoku, and N-Queens problems.
This document discusses constraint satisfaction problems (CSP) and the CSP solving technique called forward checking. It provides an example of a map coloring CSP problem and then explains forward checking, which tracks remaining legal values for unassigned variables and terminates the search when a variable has no legal values left. It also discusses using heuristics like the degree heuristic, minimum remaining values heuristic, and least constraining value heuristic to guide the search order during forward checking.
Constraint Satisfaction Problems (CSPs) involve variables with domains of possible values and constraints specifying allowed value combinations. The document discusses CSP definitions and representations, examples like Sudoku and graph coloring, and solutions being complete consistent assignments. It also covers backtracking search for CSPs, heuristics like minimum remaining values and least constraining value, and forward checking for pruning inconsistent values earlier.
This document provides an overview of stochastic processes and Markov chains. It defines stochastic processes as families of random variables indexed by time. Markov chains are a type of stochastic process where the future state depends only on the present state, not on the past. The document discusses examples of Markov chains, transition matrices, classification of states as transient or persistent, and properties like irreducibility. It aims to introduce key concepts in stochastic processes and Markov chains.
This document discusses constraint satisfaction problems (CSPs). It defines CSPs as problems with variables that must satisfy constraints. CSPs can represent many real-world problems and are solved through constraint satisfaction methods. The document outlines CSP components like variables, domains, and constraints. It also describes representing problems as CSPs, solving CSPs through backtracking search, and the role of heuristics like minimum remaining values in improving the search process.
This document describes constraint satisfaction problems (CSPs) and techniques for solving them. CSPs model problems as variables with domains where the goal is to assign values in a way that satisfies constraints. Standard search algorithms like depth-first search can solve CSPs but are inefficient. More specialized CSP algorithms use filtering to prune values that cannot lead to solutions, enforcing consistency constraints. Variable and value ordering heuristics like minimum remaining values (MRV) and least constraining value (LCV) can significantly improve search performance. Demos illustrate CSP formulations and solving techniques.
Slides from my survey talk on Backdoors to SAT at the pre-conference workshop on New Developments in Exact Algorithms and Lower Bounds at FSTTCS 2014 in Delhi.
Effect of global market on indian marketArpit Jain
This document summarizes a study that uses Granger's causality test to analyze the impact of the Nasdaq, Hang Seng, and Nikkei stock market indices on India's Sensex index. It first provides background on time series analysis and challenges in determining stationarity and causality. It then explains key concepts like correlograms, unit roots, and random walks. The document outlines the Granger causality test methodology and reports the main results, finding causality from the Nasdaq and Nikkei to the Sensex, and from the Sensex to the Hang Seng. It concludes by noting limitations around selecting the optimal number of lags.
Bounded model checking encodes executions of a system up to a bounded length k as a propositional formula along with a property violation. If the formula is satisfiable, a counterexample is found; if unsatisfiable, no counterexample up to length k exists. The technique leverages efficient SAT solvers but is incomplete. Modern SAT solvers use conflict-driven learning and backtracking based on the Davis-Putnam-Logemann-Loveland algorithm to efficiently solve the propositional formulas generated by bounded model checking.
Avionics 738 Adaptive Filtering at Air University PAC Campus by Dr. Bilal A. Siddiqui in Spring 2018. This lecture covers background material for the course.
The Gaussian wavelet is defined as the derivative of the Gaussian probability density function. It belongs to a family of Hermitian wavelets used in continuous wavelet transforms. The nth Gaussian wavelet is the nth derivative of the Gaussian function. Gaussian wavelets have no scaling function and are not orthogonal or compactly supported, making the discrete wavelet transform and perfect reconstruction impossible. However, the continuous wavelet transform can be used to detect discontinuities in signals using Gaussian wavelets.
1. Recurrent neural networks (RNNs) allow information to persist from previous time steps through hidden states and can process input sequences of variable lengths. Common RNN architectures include LSTMs and GRUs which address the vanishing gradient problem of traditional RNNs.
2. RNNs are commonly used for natural language processing tasks like machine translation, sentiment classification, and named entity recognition. They learn distributed word representations through techniques like word2vec, GloVe, and negative sampling.
3. Machine translation models use an encoder-decoder architecture with an RNN encoder and decoder. Beam search is commonly used to find high-probability translation sequences. Performance is evaluated using metrics like BLEU score.
Elements of Inference covers the following concepts and takes off right from where we left off in the previous slide https://www.slideshare.net/GiridharChandrasekar1/statistics1-the-basics-of-statistics.
Population Vs Sample (Measures)
Probability
Random Variables
Probability Distributions
Statistical Inference – The Concept
This document proposes fast single-pass k-means clustering algorithms to allow for fast nearest neighbor search on large datasets. It discusses the rationale for using k-means clustering, describes algorithms like ball k-means and surrogate methods that can perform clustering in a single pass. It covers implementations using techniques like locality sensitive hashing and projection search to speed up vector searches. Evaluation on synthetic and real datasets shows the algorithms can achieve the same or better accuracy as traditional k-means 10x faster, enabling applications like fast nearest neighbor search on massive datasets for applications like customer modeling.
This document discusses the k-nearest neighbors (k-NN) algorithm. It begins by explaining the basic principles of k-NN, including that records close to each other in a data space will be of the same type. It then discusses issues with k-NN like computational expense, storage requirements, and performance with high-dimensional data. The document goes on to discuss techniques to improve k-NN, including condensing the training data set to reduce redundant points while retaining the decision boundary, and using proximity graphs and editing algorithms to further refine the training set.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
2. Constraint satisfaction problems (CSPs)
• Standard search problem: state is a "black box“ – any data
structure that supports successor function and goal test
• CSP:
– state is defined by variables Xi with values from domain Di
– goal test is a set of constraints specifying allowable combinations
of values for subsets of variables
• Simple example of a formal representation language
• Allows useful general-purpose algorithms with more
power than standard search algorithms
3. Example: Map-Coloring
• Variables WA, NT, Q, NSW, V, SA, T
• Domains Di = {red,green,blue}
• Constraints: adjacent regions must have different colors
• e.g., WA ≠ NT, or (WA,NT) in {(red,green),(red,blue),(green,red),
(green,blue),(blue,red),(blue,green)}
4. Example: Map-Coloring
• Solutions are complete and consistent assignments
• e.g., WA = red, NT = green, Q = red, NSW =
green,V = red,SA = blue,T = green
•
5. Constraint graph
• Binary CSP: each constraint relates two variables
• Constraint graph: nodes are variables, arcs are constraints
6. Varieties of CSPs
• Discrete variables
– finite domains:
• n variables, domain size d O(dn) complete assignments
• e.g., Boolean CSPs, incl. Boolean satisfiability (NP-complete)
– infinite domains:
• integers, strings, etc.
• e.g., job scheduling, variables are start/end days for each job
• need a constraint language, e.g., StartJob1 + 5 ≤ StartJob3
• Continuous variables
– e.g., start/end times for Hubble Space Telescope observations
– linear constraints solvable in polynomial time by LP
7. Varieties of constraints
• Unary constraints involve a single variable,
– e.g., SA ≠ green
• Binary constraints involve pairs of variables,
– e.g., SA ≠ WA
• Higher-order constraints involve 3 or more
variables,
– e.g., cryptarithmetic column constraints
8. Backtracking search
• Variable assignments are commutative, i.e.,
[ WA = red then NT = green ] same as [ NT = green then WA = red ]
• => Only need to consider assignments to a single variable at
each node
• Depth-first search for CSPs with single-variable assignments
is called backtracking search
• Can solve n-queens for n ≈ 25
13. Improving backtracking efficiency
• General-purpose methods can give huge
gains in speed:
– Which variable should be assigned next?
– In what order should its values be tried?
– Can we detect inevitable failure early?
14. Most constrained variable
• Most constrained variable:
choose the variable with the fewest legal values
• a.k.a. minimum remaining values (MRV)
heuristic
15. Most constraining variable
• A good idea is to use it as a tie-breaker
among most constrained variables
• Most constraining variable:
– choose the variable with the most constraints on
remaining variables
–
16. Least constraining value
• Given a variable to assign, choose the least
constraining value:
– the one that rules out the fewest values in the
remaining variables
–
• Combining these heuristics makes 1000
queens feasible
17. Forward checking
• Idea:
– Keep track of remaining legal values for unassigned variables
– Terminate search when any variable has no legal values
–
18. Forward checking
• Idea:
– Keep track of remaining legal values for unassigned variables
– Terminate search when any variable has no legal values
–
19. Forward checking
• Idea:
– Keep track of remaining legal values for unassigned variables
– Terminate search when any variable has no legal values
–
20. Forward checking
• Idea:
– Keep track of remaining legal values for unassigned variables
– Terminate search when any variable has no legal values
–
21. Constraint propagation
• Forward checking propagates information from assigned to
unassigned variables, but doesn't provide early detection
for all failures:
•
• NT and SA cannot both be blue!
• Constraint propagation algorithms repeatedly enforce
constraints locally…
22. Arc consistency
• Simplest form of propagation makes each arc consistent
• X Y is consistent iff
•
for every value x of X there is some allowed y
23. Arc consistency
• Simplest form of propagation makes each arc consistent
• X Y is consistent iff
•
for every value x of X there is some allowed y
24. Arc consistency
• Simplest form of propagation makes each arc consistent
• X Y is consistent iff
•
for every value x of X there is some allowed y
• If X loses a value, neighbors of X need to be rechecked
25. Arc consistency
• Simplest form of propagation makes each arc consistent
• X Y is consistent iff
•
for every value x of X there is some allowed y
• If X loses a value, neighbors of X need to be rechecked
• Arc consistency detects failure earlier than forward checking
• Can be run as a preprocessor or after each assignment
26. Arc consistency algorithm AC-3
• Time complexity: O(#constraints |domain|3)
Checking consistency of an arc is O(|domain|2)
27. k-consistency
• A CSP is k-consistent if, for any set of k-1 variables, and for any consistent
assignment to those variables, a consistent value can always be assigned to
any kth variable
• 1-consistency is node consistency
• 2-consistency is arc consistency
• For binary constraint networks, 3-consistency is the same as path consistency
• Getting k-consistency requires time and space exponential in k
• Strong k-consistency means k’-consistency for all k’ from 1 to k
– Once strong k-consistency for k=#variables has been obtained, solution
can be constructed trivially
• Tradeoff between propagation and branching
• Practitioners usually use 2-consistency and less commonly 3-consistency
28. Other techniques for CSPs
• Global constraints
– E.g., Alldiff
– E.g., Atmost(10,P1,P2,P3), i.e., sum of the 3 vars ≤ 10
– Special propagation algorithms
• Bounds propagation
– E.g., number of people on two flight D1 = [0, 165] and D2 = [0, 385]
– Constraint that the total number of people has to be at least 420
– Propagating bounds constraints yields D1 = [35, 165] and D2 = [255, 385]
• …
• Symmetry breaking
33. Tree decomposition
• Algorithm: solve for all solutions of each subproblem. Then, use the tree-
structured algorithm, treating the subproblem solutions as variables for those
subproblems.
• O(ndw+1) where w is the treewidth (= one less than size of largest subproblem)
• Finding a tree decomposition of smallest treewidth is NP-complete, but good
heuristic methods exists
• Every variable in original
problem must appear in at least
one subproblem
• If two variables are connected
in the original problem, they
must appear together (along
with the constraint) in at least
one subproblem
• If a variable occurs in two
subproblems in the tree, it must
appear in every subproblem on
the path that connects the two
35. Davis-Putnam-Logemann-Loveland
(DPLL) tree search algorithm
E.g. for 3SAT
? s.t. (p1p3p4) (p1p2p3) …
Backtrack when some clause becomes empty
Unit propagation (for variable & value ordering): if some clause
only has one literal left, assign that variable the value that satisfies
the clause (never need to check the other branch)
Boolean Constraint Propagation (BCP): Iteratively apply unit
propagation until there is no unit clause available
p p1
p3
p2
p4
F
F
T
T
Complete
clause
36. A helpful observation for the
DPLL procedure
P1 P2 … Pn Q (Horn)
is equivalent to
(P1 P2 … Pn) Q (Horn)
is equivalent to
P1 P2 … Pn Q (Horn clause)
Thrm. If a propositional theory consists only of Horn clauses
(i.e., clauses that have at most one non-negated variable) and
unit propagation does not result in an explicit contradiction
(i.e., Pi and Pi for some Pi), then the theory is satisfiable.
Proof. On the next page.
…so, Davis-Putnam algorithm does not need to branch on
variables which only occur in Horn clauses
37. Proof of the thrm
Assume the theory is Horn, and that unit propagation has completed
(without contradiction). We can remove all the clauses that were satisfied
by the assignments that unit propagation made. From the unsatisfied
clauses, we remove the variables that were assigned values by unit
propagation. The remaining theory has the following two types of clauses
that contain unassigned variables only:
P1 P2 … Pn Q and
P1 P2 … Pn
Each remaining clause has at least two variables (otherwise unit
propagation would have applied to the clause). Therefore, each remaining
clause has at least one negated variable. Therefore, we can satisfy all
remaining clauses by assigning each remaining variable to False.
38. Variable ordering heuristic for DPLL [Crawford & Auton AAAI-93]
Heuristic: Pick a non-negated variable that occurs in a non-
Horn (more than 1 non-negated variable) clause with a
minimal number of non-negated variables.
Motivation: This is effectively a “most constrained first”
heuristic if we view each non-Horn clause as a “variable”
that has to be satisfied by setting one of its non-negated
variables to True. In that view, the branching factor is the
number of non-negated variables the clause contains.
Q: Why is branching constrained to non-negated variables?
A: We can ignore any negated variables in the non-Horn
clauses because
– whenever any one of the non-negated variables is set to True the
clause becomes redundant (satisfied), and
– whenever all but one of the non-negated variables is set to False
the clause becomes Horn.
Variable ordering heuristics can make several orders of
magnitude difference in speed.
39. Constraint learning aka nogood learning aka clause learning
used by state-of-the-art SAT solvers (and CSP more generally)
Conflict graph
• Nodes are literals
• Number in parens shows the search tree level
where that node got decided or implied
• Cut 2 gives the first-unique-implication-point (i.e., 1 UIP on reason side) constraint
(v2 or –v4 or –v8 or v17 or -v19). That schemes performs well in practice.
Any cut would give a valid clause. Which cuts should we use? Should we delete some?
• The learned clauses apply to all other parts of the tree as well.
40. Conflict-directed backjumping
• Then backjump to the decision level of x3=1,
keeping x3=1 (for now), and
forcing the implied fact x7=0 for that x3=1 branch
• WHAT’S THE POINT? A: No need to just backtrack to x2
Failure-driven assertion (not a branching decision):
Learned clause is a unit clause under this path, so
BCP automatically sets x7=0.
x7=0
x2=0
41. Classic readings on conflict-directed backjumping,
clause learning, and heuristics for SAT
• “GRASP: A Search Algorithm for Propositional Satisfiability”,
Marques-Silva & Sakallah, IEEE Trans. Computers, C-48,
5:506-521,1999. (Conference version 1996.)
• (“Using CSP look-back techniques to solve real world SAT
instances”, Bayardo & Schrag, Proc. AAAI, pp. 203-208, 1997)
• “Chaff: Engineering an Efficient SAT Solver”, Moskewicz,
Madigan, Zhao, Zhang & Malik, 2001
(www.princeton.edu/~chaff/publication/DAC2001v56.pdf)
• “BerkMin: A Fast and Robust Sat-Solver”, Goldberg &
Novikov, Proc. DATE 2002, pp. 142-149
• See also slides at
http://www.princeton.edu/~sharad/CMUSATSeminar.pdf
42. More on conflict-directed backjumping (CBJ)
• These are for general CSPs, not SAT specifically:
• Read Section 6.3.3. of Russell & Norvig for an easy description of
conflict-directed backjumping for general CSP
• “Conflict-directed backjumping revisited” by Chen and van Beek, Journal
of AI Research, 14, 53-81, 2001:
– As the level of local consistency checking (lookahead) is increased, CBJ
becomes less helpful
• A dynamic variable ordering exists that makes CBJ redundant
– Nevertheless, adding CBJ to backtracking search that maintains generalized
arc consistency leads to orders of magnitude speed improvement
experimentally
• “Generalized NoGoods in CSPs” by Katsirelos & Bacchus, National
Conference on Artificial Intelligence (AAAI-2005) pages 390-396, 2005.
– This paper generalizes the notion of nogoods, and shows that nogood learning
(then) can speed up (even non-SAT) CSPs significantly
43. Random restarts
• Sometimes it makes sense to keep restarting
the CSP/SAT algorithm, using
randomization in variable ordering
– Avoids the very long run times of unlucky
variable ordering
– On many problems, yields faster algorithms
– Clauses learned can be carried over across
restarts
– Experiments suggest it does not help on
optimization problems (e.g., [Sandholm et al.
IJCAI-01, Management Science 2006])
45. “Order parameter” for 3SAT
[Mitchell, Selman, Levesque AAAI-92]
• b = #clauses / # variables
• This predicts
– satisfiability
– hardness of finding a model
46.
47. How would you capitalize on the
phase transition in an algorithm?
48. Generality of the order parameter b
• The results seem quite general across model
finding algorithms
• Other constraint satisfaction problems have
order parameters as well
49. …but the complexity peak does not occur
(at least not in the same place) under all
ways of generating SAT instances
51. GSAT [Selman, Levesque, Mitchell AAAI-92]
(= a local search algorithm for model finding)
Incomplete (unless restart a lot)
2000
1600
1200
800
400
Avg. total flips
100 200
50 variables, 215 3SAT clauses
max-climbs
Greediness is not essential as long
as climbs and sideways moves are
preferred over downward moves.
52. BREAKOUT algorithm [Morris AAAI-93]
Initialize all variables Pi randomly
UNTIL current state is a solution
IF current state is not a local minimum
THEN make any local change that reduces the total cost
(i.e. flip one Pi)
ELSE increase weights of all unsatisfied clause by one
Incomplete, but very efficient on large (easy) satisfiable problems.
Reason for incompleteness: the cost increase of the current local
optimum spills over to other solutions because they share
unsatisfied clauses.