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# Simplified algorithm on network shortest path problem

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• 1. Simplified Algorithm on Network Shortest PathProblemABSTRACT:An algorithm on the network shortest path problem by gradually eliminating loops on anetwork is put forward. Using the wagon routing arrowhead line, we start from the origin,plot the routing arrowhead lines in the current loop and the adjacent loops, and decidewhich edge the arrowhead pointed to should be moved; then according to the structure ofthe candidate edges to be removed and certain regulations, remove one edge to enlargethe current loop; select the loop nearest to the origin and repeat the above process, untilobtain the shortest routing tree taking the origin as its root. The cast study carried outshows that the algorithm is simple, practical, knowable, and suitable for manualsearching the shortest route on a simple non-directional network.Existing System:• Existing system uses RTF and RTC built up for discretization error along a path.• Here efficiency of the algorithms directly relates to the magnitudeof the errors introduced during discretization .Proposed System:• In our project we use two techniques to decrease the discretion error.• Here we use randomized discretization and path delay discretization techniques.• The above new techniques either make the link errors to cancel out each otheralong the path or treat the path delay as a whole for discretization, which results inmuch smaller errors.www.nanocdac.com www.nsrcnano.com branches: hyderabad nagpur
• 2. • The algorithms based on these techniques run much faster than the best existingalgorithmSystem Requirements:Hardware:PROCESSOR : PENTIUM IV 2.6 GHzRAM : 512 MB DD RAMMONITOR : 15” COLORHARD DISK : 20 GBCDDRIVE : LG 52XKEYBOARD : STANDARD 102 KEYSMOUSE : 3 BUTTONSSoftware:FRONT END : SWINGS,JFRAMEBUILDER.OPERATING SYSTEM : Window’s XpBACK END : Sql Server 2000Modules:• Design of LAN structure• Finding all possible path• Time calculation• Random discriminationwww.nanocdac.com www.nsrcnano.com branches: hyderabad nagpur
• 3. Module Description:Design of LAN structure:Here we design the structure for which the shortest path is to find .thestructure to which we find the shortest path is drawn beIn the data flow diagram.Finding all possible paths:Consider a network, where is a set of nodes and is a set of directed links connecting thenodes. The delay and the cost of a link are denoted as and , respectively. The delay andthe cost of a path are denoted as and , respectively. and. Let be the length (number ofhops) of , and be the length of the longest path in the network. Given a delay requirement,is called a feasible path if . Given a source node, let be the set of nodes to which thereexist feasible paths from . For any , the cheapest feasible path from to is defined as Thedelay-constrained least-cost routing problem (DCLC) is to find the cheapest feasiblepaths from to all nodes in which is NP-complete [19]. However, if the link delays are allintegers and the delay requirement is bounded by an integer , the problem can be solvedin time by Joksch’s dynamic programming algorithm [20] or the extended Dijkstra’salgorithm [17].Joksch’s algorithm is described as follows. , let be a variable storing thecost of the cheapest path from to with , and storing the last link of the path.Initially,and .NIL. Assuming that all link delays are positive, the dynamic programmingis given below. Now suppose the link delays are allowed to be zero. We need to add onemore step. Let be the sub graph consisting of all zero-delay links. For each , immediatelyafter Joksch’s algorithm calculates , Dijkstra’s algorithm is executed on to improve onzero-delay paths [18].The above polynomials solvable special case with integer delayspoints out a heuristic solution for the general NP-complete problem with arbitrary delays.The idea is to discretize (scale and then round) arbitrary link delays to integers [15], [17],www.nanocdac.com www.nsrcnano.com branches: hyderabad nagpur
• 4. [18], [21]. There are two existing discrimination approaches, round to ceiling [17] andround to floor [18]. Both approaches map the delay requirement to a selected integer ,and then discretize the link delays as follows.Time calculationRTC creates negative rounding errors on links. The error accumulates along a path. Theaccumulated error is proportional to the path length. The larger the topology, the longer apath, the larger the accumulated error. The same thing is true for RTF,which has positiverounding errors on links. In order to achieve -approximation, the accumulated error on apath cannot be too large. To reduce the error on a path, the existing algorithms based onRTC or RTF must reduce the discrimination errors on the links by using a large value.Given the time complexity proportion to .The insight is that if we can reduce the errorintroduced by discretization without using a larger , we can improve the performance ofthe algorithm.We develop two new techniques. The first one is called randomizeddiscretization. It rounds to ceiling or to floor according to certain probabilities. The ideais for some links to have positive errors and some links to have negative errors. Positiveerrors and negative errors cancel out one another along a path in such a way that theaccumulated error is minimized statistically. We will prove that, when the followingdiscretization approach is used, the mean of the accumulated error on a path is zero andthe standard deviation is bounded . In comparison, the mean of the accumulated error isfor RTC and for RTF.Technique used or algorithm used:• RANDOMIZED DISCRETIZATION• PATH DELAY DISCRETIZATIONwww.nanocdac.com www.nsrcnano.com branches: hyderabad nagpur
• 5. Advantages:• Shortest path is found using time.• Shortest path varies according to the congestion occurred in the path.REFERENCE:Xie Jin-bao, “Simplified Algorithm on Network Shortest Path Problem”, IEEEConference 2011.www.nanocdac.com www.nsrcnano.com branches: hyderabad nagpur
• 6. Advantages:• Shortest path is found using time.• Shortest path varies according to the congestion occurred in the path.REFERENCE:Xie Jin-bao, “Simplified Algorithm on Network Shortest Path Problem”, IEEEConference 2011.www.nanocdac.com www.nsrcnano.com branches: hyderabad nagpur