PPT-CSE 322: Shortest Paths

Richard Anderson Spring 2016 Announcements 2 3 Graphs A formalism for representing relationships between objects Graph G VE Set of vertices V v 1 v 2 v. Slide . 1. Bottom Up: Soundness and Completeness. Computer Science cpsc322, Lecture 21. (Textbook . Chpt. 5.2). March, 5, 2010. CPSC 322, Lecture 21. Slide . 2. Lecture Overview. Recap. Soundness of Bottom-up Proofs. F. n. = F. n-1. + F. n-2. F. 0 . =0, F. 1 . =1. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 … . Straightforward recursive procedure is slow!. Why? How slow? . Let’s draw the recursion tree. Fibonacci Numbers (2). in Dynamic Graphs. Viswanath. . Gunturi. (4192285). Bala. . Subrahmanyam. . Kambala. (4451379) . Application Domain. Transportation Networks:. Sample Dataset. Sample dataset showing the dynamic nature . Abhilasha Seth. CSCE 669. Replacement Paths. G = (V,E) - directed graph with positive edge weights. ‘s’, ‘t’ - specified vertices. π. (s, t) - shortest path between them. Replacement Paths:. Basic Categories. Single source vs. all-pairs. Single Source Shortest Path: SSSP. All-pairs Shortest Path: APSP. Weighted vs. unweighted. Can edges be negative?. Can there be negative cycles?. Often, . Slide . 1. Reasoning Under Uncertainty: Belief Networks. Computer Science cpsc322, Lecture 27. (Textbook . Chpt. 6.3). March, . 22, 2010. CPSC 322, Lecture 2. Slide . 2. Big Picture: R&R systems. The discrete way. © Alexander & Michael Bronstein, 2006-2009. © . Michael . Bronstein, 2010. tosca.cs.technion.ac.il/book. 048921 Advanced topics in vision. Processing . and Analysis of Geometric Shapes. . Paths. :. Basics. Algorithms. and Networks 2016/2017. Johan M. M. van Rooij. Hans L. . Bodlaender. Shortest path problem(s). Undirected single-pair shortest path problem. Given a graph G=(V,E) and a length function . Discrete Dynamic Programming. Example 9.1 . Littleville. Suppose . that you are the city traffic engineer for the town of . Littleville. . Figure . 9.1(a. ) depicts the arrangement of one- and two-way streets in a proposed improvement plan for . Shortest Path Algorithm Lecture 20 CS2110. Spring 2019 1 Type shortest path into the JavaHyperText Filter Field A6. Implement shortest-path algorithm One semester: mean time: 4.2 CPSC 322, Lecture 14 Slide 1 Local Search Computer Science cpsc322, Lecture 14 (Textbook Chpt 4.8) Oct, 7, 2013 Department of Computer Science Undergraduate Events More details @ https://www.cs.ubc.ca/students/undergrad/life/upcoming-events 1. Introduction to. Artificial Intelligence (AI). Computer Science cpsc322, Lecture 1. Sept, 5, 2012. CPSC 322, Lecture 1. Slide . 2. People. Instructor. Giuseppe . Carenini. . ( carenini@cs.ubc.ca;  office CICSR 105). Shortest Path problem. Given a graph G, edges. have length w(. u,v. ) > 0.. (distance, travel time, . cost, … ). Length of a path is equal. to the sum of edge. lengths. Goal: Given source . s. and destination . Computer Science cpsc422, Lecture 20. Mar, 3, 2021. Slide credit: some slides adapted from . Stuart Russell (Berkeley), some from . Padhraic. Smyth (. UCIrvine. ). 422 big picture. Query. Planning.