Algorithms for Shortest Paths. course web page: piazza: Learn - for marks. Lecture 1. CS 860 Fall Anna Lubiw, U. Waterloo.
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1 CS 860 Fall 2014 Algorithms for Shortest Paths course web page: piazza: Learn - for marks desire path
2 Historical Columbus Anasazi
3 Topics Intro and Dijkstra's algorithm basic algorithms for geometric shortest paths basic algorithms for graph shortest paths more graph shortest path algorithms: all pairs, kth shortest, planar graphs, forbidden pairs, etc. more geometric shortest path algorithms: link distance, polyhedral surfaces, 3D, weighted region, etc. further topics spanners network routing reconfiguration problems touring (TSP) and etc.
4 Topics basic algorithms for geometric shortest paths Polygon Polygonal Domain S S T T O(n) Θ(n log n) fixed target versus query versions
5 Topics basic algorithms for graph shortest paths Dijkstra, Bellman-Ford more graph shortest path algorithms: all pairs Timothy Chan.1 (a) Ingredientsandtoolsusedforrealizingagraph:balls,strings,scissorsanda Camil Demetrescu Giuseppe F. Italiano kth shortest David Eppstein, Finding the k shortest paths, cited by 1293 planar graphs forbidden pairs etc. maybe disjoint paths
6 Topics more geometric shortest path algorithms: link distance polyhedral surfaces 3D weighted region etc.
7 Topics further topics spanners - make graph less dense while approximately preserving distances network routing reconfiguration problems, diameter touring (TSP) and etc.
8 Credit requirements 2 assignments (20%) presentation of 1 paper (30%) - 30 minutes + discussion exploration of open question (20%) - written report, approx. 2 pages. Formulate a good open question and suggest how to tackle it. BONUS if you succeed. mini reviews of presented papers (30%) - half page reports, submitted through Piazza.
9 Shortest Paths in Graphs Input: a graph G=(V,E) with weights w:e > R on edges, vertices s, t Find the shortest [simple] path from s to t. NP-complete in general polynomial time for - directed acyclic graphs - non-negative weights - graphs with no negative weight cycle
10 Dijkstra s Shortest Path Algorithm Idea Correctness Implementations basic heap Fibonacci heap
11 Dijkstra s paper A note on two problems in connexion with graphs EW Dijkstra - Numerische mathematik, Springer Cited by Related articles All 13 versions From: for some history, see: The Quest for the Shortest Route C Demetrescu, GF Italiano - The Power of Algorithms, Springer Dijkstra: From: At the time, algorithms were hardly considered a scientific topic. I wouldn t have known where to publish it.... The mathematical culture of the day was very much identified with the continuum and infinity. Could a finite discrete problem be of any interest? The number of paths from here to there on a finite graph is finite; each path is a finite length; you must search for the minimum of a finite set. Any finite set has a minimum next problem, please. It was not considered mathematically respectable... read his paper write a mini-review
12 other implementations of Dijkstra s algorithm Dial s method DIAL, R. Algorithm 360: Shortest path forest with topological ordering. Commun. ACM 12 (1969),
13 other implementations of Dijkstra s algorithm Dial s method reducing space from nc to C+1
14 other implementations of Dijkstra s algorithm double bucket method DENARDO, E. V., AND Fox, B. L. Shortest-route methods: 1. Reaching, pruning, and buckets. Oper.Res. 27(1979),
15 related papers to present Faster algorithms for the shortest path problem RK Ahuja, K Mehlhorn, J Orlin, RE Tarjan - Journal of the ACM (JACM), dl.acm.org Cited by 551 Related articles All 19 versions Cite Save From: Undirected single-source shortest paths with positive integer weights in linear time M Thorup - Journal of the ACM (JACM), dl.acm.org Cited by 307 Related articles All 11 versions Cite Save From: +Time&btnG=&hl=en&as_sdt=0%2C5 Shortest paths algorithms: Theory and experimental evaluation BV Cherkassky, AV Goldberg, T Radzik - Mathematical programming, Springer Cited by 781 Related articles All 36 versions Cite Save From: Computing the shortest path: A* search meets graph theory AV Goldberg, C Harrelson - Proceedings of the sixteenth annual ACM-, dl.acm.org Cited by 462 Related articles All 20 versions Cite Save From: [HTML] Trans-dichotomous algorithms for minimum spanning trees and shortest paths ML Fredman, DE Willard - Journal of Computer and System Sciences, Elsevier Cited by 282 Related articles All 4 versions Cite Save From:
16 accessing papers from home
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