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Title: CS235102 Data Structures Author: Gary Last modified by: Luse Cheng Created Date: 3/20/2005 9:13:01 AM Document presentation format:

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Shortest Paths Text Discrete Mathematics and Its Applications (5th Edition) Kenneth H. Rosen Chapter 10.6 Based on s from Chuck Allison, Michael T. Goodrich, and ...

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The Traveling Salesman Problem Importance: Variety of scheduling application can be solved as a traveling salesmen problem. Examples: ...

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Title: Discrete Structures - CSIS121 Author: e. carey Last modified by: Longin Jan Latecki Created Date: 3/7/1998 11:53:18 PM Document presentation format

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Shortest Path Problems Directed weighted graph. Path length is sum of weights of edges on path. The vertex at which the path begins is the source vertex.

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Shortest Path Problems Directed weighted graph. Path length is sum of weights of edges on path. The vertex at which the path begins is the source vertex.

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Friday is Halloween. Why did I receive a Christmas card on Halloween? Shortest Paths Lecture 19 CS2110 Fall2014

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Let Lm(i,j) denote the length of the shortest path from node i to node j using at most m edges ... in terms of Lm(i,j)? What is a recurrence relation for Lm(i,j) ...

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Title: PowerPoint Presentation Author: Juris Last modified by: katia Created Date: 10/16/2000 4:49:17 PM Document presentation format: Apresenta o na tela

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... G=(V,E), length for each edge e in E, w(e) Distance from u to v: length of shortest path ... Solving SSSP problem with negative edge lengths; use Bellman-Ford. ...

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Unprocessed node adjacent to. 4 is 6. 70 55 10 = 65. so replace 70 with 65 ... Unprocessed node adjacent to. 6 is 7. 95 65 15 = 80. so replace 95 with 80 ...

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Shortest Paths Lecture 19 CS2110 Spring 2015 Here s a bit of history about Dijkstra s shortest path algorithm. Dijkstra was 26 at the time.

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Lecture 6 Dijkstra s Algorithm for the Shortest Path Problem Update 1 2 4 6 2 4 2 1 3 4 2 3 2 0 3 2 3 6 4 5 6 0 1 2 3 4 5 6 7 6 4 5 6 Choose Minimum ...

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Title: Data Representation Methods Author: Preferred Customer Last modified by: sahni Created Date: 6/17/1995 11:31:02 PM Document presentation format

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FLIGHT TIMES. 4:05. 2:55. 2:20. 2:10. 3:50. 2:00. 1:15. 2:10. 1:40. 1:30. 1:55. 2:45. 0:50. 1:50 ... The length of a path in a weighted graph is the sum of the ...

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Shortest Path Algorithm 2 Prof. Sin-Min Lee Department of Computer Science Greed: Shortest Path Directed Graph Directed graph: G = (V, E) . V = set of vertices or nodes.

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All-pairs Shortest Paths

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We now know the shortest distance. from V0 to one other vertex, V4. 4. Updating W. W ... Once we have evaluated one vertex. we go looking for another. ...

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All-Pairs Shortest Paths ... When there is a cycle whose length is 0, some shortest paths aren't finite. ... vertex on i to k and k to j paths is k-1. ...

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Optimal substructure property. All sub-paths of shortest paths are shortest paths. ... d(x, y) d*(y, v) optimal substructure d*(s, x) d(x, y) nonnegative lengths ...

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Dynamic (All Pairs) Shortest Paths. Given a weighted directed graph G=(V,E,w) ... Properties of Uniform paths. For the sake ... Uniform paths in dynamic graphs ...

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Shortest Paths (Review) Update rule: Let a' be the ... BWI. PVD. 867. 2704. 187. 1258. 849. 144. 740. 1391. 184. 946. 1090. 1121. 2342. 1846. 621. 802. 1464 ...

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Items are produced in batches of B 0 items. ... fij per batch, plus. gij per item in the batch. When should we inspect to minimize total costs? ...

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Shortest Path. Dijkstra's Algorithm. finds the shortest path from the start ... To find the shortest path from A to G, start from G and work backwards, using ...

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If the weights of all edges are all the same, then breadth-first search can be ... Bellman-Ford SSSP algorithm can handle negative edge weights. ...

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MIA. 337. 2704. 1846. 1464. 1235. 2342. 802. 867. 849. 740. 187. 144. 1391. 184. 1121. 946. 1090. 1258 ... MIA. 946. 337. 2704. 1846. 1464. 1235. 2342. 802 ...

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Chapter 26 All-Pairs Shortest Paths Problem definition Shortest paths and matrix multiplication The Floyd-Warshall algorithm Problem definition: Real problem:When to ...

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Chapter 24: Single-Source Shortest-Path

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Title: Data Representation Methods Author: Preferred Customer Last modified by: sahni Created Date: 6/17/1995 11:31:02 PM Document presentation format

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Shortest Path and Minimum Spanning Tree HKOI Training 2009 7 Feb 2009

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Chapter 25: All-Pairs Shortest Paths Application: Computing distance table for a road atlas. Atlanta Chicago Detroit Atlanta - 650 ...

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Shortest Path Problems: Floyd-Warshall Algorithm for the All-Pairs Shortest Path Problem with Arbitrary Arc Costs Updated 18 February 2008 Floyd-Warshall Algorithm ...

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Assume that d(u) and d(v) are finite ... Assume that source s is connected to every vertex in the graph, and all edge ... Assume that the graph has no cycles of ...

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Title: Coloring k-colorable graphs using smaller palletes Author: Uri Zwick Last modified by: Uri Zwick Created Date: 8/8/2000 8:53:06 AM Document presentation format

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Open Shortest Path First OSPF OSPF Overview OSPF Operation By Grace Deng Oct.16.2003 OSPF Overview History Development began 1987 by IETF Goal a link state protocol ...

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Open Shortest Path First. OSPF (Part 2) George Macri. E-mail: gmacri ... Open Shortest Path First (OSPF) Protocol. Enhanced IGRP (EIGRP) Application. Transport ...

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However, Dijkstra's always visits the vertex with the smallest distance next, so ... Certainly this is a generalization of Dijkstra's. ...

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Shortest Path Algorithms. Jim E. Jones. Talk Outline. Background for the ... for (k = 0; k n; k ) for (i = 0; i n; i ) for (j = 0; ... dIK. dKJ ...

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Lecture 22: Matrix Operations and All-pair Shortest Paths II Shang-Hua Teng Matrix Multiplication Add and Multiply Rings: Commutative, Associative Distributive Other ...

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Department of Computer Science & Information ... Let P(i, j) be the shortest path between i and j. ... Case1: If k is not an intermediate vertex of P ...

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application of single source shortest path algorithms. direct methods to solve the problem: ... table of distances between all pairs of cities for a road atlas ...

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If no negative-weight cycles reachable from the source s, then for all v V, the ... reachable from a vertex whose shortest path is - ,it,too,has a shortest-path weight ...

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Stochastic Learning Automata-Based Dynamic Algorithms for Single Source Shortest Path Problems S. Misra B. John Oommen Professor and Fellow of the IEEE

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Shortest-Path Property 4.1. If the path s - n1 - n2 - ... - nk is a shortest path from s to k, then the ... Converse Property. Suppose d(j) = d(i) cij for ...

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w: E R mapping edges to real valued weights. Graph Algorithms: Shortest Path. 1. 2. 3 ... this problem efficiently for the case in which all weights are ...

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The Shortest Path Problem * * * * * * Cpt S 223. School of EECS, WSU Cpt S 223 Washington State University Cpt S 223 Washington State University Cpt S 223 Washington ...

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Idea #3: If Dk(i,j) is the shortest path between vertex i and vertex j using ... Assume that we have Dk-1(i,j) for all i, and j. We wish to compute Dk(i,j) ...

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Single-Source Shortest Paths (25/24) HW: 25-2 and 25-3 p. 546/24-2 and 24-3 p.615 Given a graph G=(V,E) and w: E weight of is w(p) = w(v[i],v[i+1])

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Shortest Path Problems. Dijkstra's Algorithm. TAT '01 Michelle Wang. Introduction. Many problems can be modeled using graphs with weights assigned to their edges: ...

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Algorithm HYPERCUBE SHORTEST PATH (A,C) Step 1: for j = 0 to n - 1 dopar ... Hypercube (Cube) Mesh. Mesh with Cut-Through Routing. Mesh with Cut-Through and ...

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Title: Chapter 26 All-Pairs Shortest Paths Author: xuying Last modified by: Windows User Created Date: 9/11/2003 9:36:11 AM Document presentation format

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Dijkstra Shortest Path Algorithm

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Repeat until all vertices have been put in the cloud: ... locators, key updates can be performed in O(logN) time. ... In terms of n, worst case time is O(n2logn) ...

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Breadth-First-Search (BFS) ... Textbook: Breadth-First Tree ... The predecessor subgraph G is a breadth-first tree if V consists of the vertices ...

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Single Source Shortest Path. Given a weighted, directed graph G = (V,E), with ... Repeatedly decreases an upper bound on the actual shortest path weight of each ...

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Developed by OSPF Working Group of IETF (not proprietary) ... T1 (1.544 Mbps seral link) 65. E1 (2.048 Mbps serial link) 48. 4 Mbps token ring 25 ...

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