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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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Friday is Halloween. Why did I receive a Christmas card on Halloween? Shortest Paths Lecture 19 CS2110 Fall2014
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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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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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Change Dijkstra's Algorithm (Slide 6) to compute the minimum distance from u to ... of 2.b (Page 323). Follow Dijkstra's Algorithm to compute the path from l ...
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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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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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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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Finding Shortest Paths Preliminary Definitions Path, Cycle, Path Length, Path Cost Problem Description Dijkstra s Algorithm Bellman-Ford Algorithm *
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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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What is the quickest route from St Austell to Launceston? Dijkstra's Algorithm ... Step 2 Give temporary labels to each vertex that is connected directly to the ...
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One source, many destinations. Examples. Methods Classification. Exact algorithms ... Shortest Pahs Maps. Fast marching method. Theory Base. Process. Algorithm ...
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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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Dijkstra Shortest Path Algorithm
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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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SINGLE-SOURCE SHORTEST PATHS Single-Source Shortest Paths in DAGs Shortest paths are always well-defined in dags no cycles = no negative-weight cycles even if there ...
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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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Shortest Path Problem For weighted graphs it is often useful to find the shortest path between two vertices Here, the shortest path is the path that has the ...
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Graphs: shortest paths & Minimum Spanning Tree(MST) 15-211 Fundamental Data Structures and Algorithms Ananda Guna April 8, 2003
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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 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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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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For weighted graphs it is often useful to find the shortest path between two vertices ... Set the cost of the start vertex to zero ...
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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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Path representation (heaps galore) Complexities of Eppstein. The problem ... Search Complexities. Finding k shortest paths from t to s. cost: O(m n log n k) ...
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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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Properties of Interest ... The path from vr to vs must be minimal (or it wouldn't exist in the shortest path) ... vr. MIN. MINs. Growing Path Length ...
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The shortest path problem is to determine the path with the minimum path length from s to t. ... This algorithm is applicable to graphs with positive arc lengths. ...
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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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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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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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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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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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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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Sort Quicksort Shortest Paths COMP 201 Formal Specification with ASML. (Examples) Hoare s quicksort Quicksort was discovered by Tony Hoare (published in 1962).
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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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Chapter 24: Single-Source Shortest-Path
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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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Iterate this procedure until all vertices are labeled. ... Iterating the procedure gives successively g=v6,d=v7,f=v8 and e=v9 .The acyclic ...
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A Shortest Path Algorithm Motivation Given a connected, positive weighted graph Find the length of a shortest path from vertex a to vertex z. Dijkstra s Shortest ...
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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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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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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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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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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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Is the shortest path problem well defined? The Dijkstra's Algorithm for Shortest Path Problem. ... { if(currentDistance(s-u) currentDistance(s-v) weight(edge(vu) ...
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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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processed nodes (distance to A is known) - active nodes (front) ... Chamfer matching: L1 distance on distance transform. Not robust at all. Hausdorff distance ...
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Dijkstra's Shortest Path Algorithm. Find shortest path from s to t. s. 3. t. 2. 6. 7. 4. 5 ... Dijkstra's Shortest Path Algorithm. s. 3. t. 2. 6. 7. 4. 5. 23 ...
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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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OSPF (Open Shortest Path First) Is an open-standards protocol, available on multiple network devices, including Cisco routers (and some switches).
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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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E E 681 - Module 5 Wayne D. Grover 2002, 2003 1 (for non-negative edge weights only) ... E E 681 - Module 5 Wayne D. Grover 2002, 2003 8. Step 7: only node ...
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It has witches, ghosts, and a floating head! We have to read a play by Shakespeare and Macbeth is the shortest and bloodiest of his plays!
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Tramp steamer problem. application: optimal ... A tramp steamer travels from port to port carrying cargo. ... Tramp-Steamer: Binary Search Procedure. Lemma. ...
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... was in junior high, we went to Washington, D.C., for the end of the year field trip. My friends and I were so excited on the second day when we got to go into ...
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