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Lecture 23

Lecture 23. CSE 331 Oct 25, 2017. Graded pitch. PAY ATTENTION TO THE COMMENTS. Shortest Path Problem. http://xkcd.com/85/. Another more important application. Is BGP a known acronym for you?. Routing uses shortest path algorithm. Shortest Path problem. s. s. s. 100.

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Lecture 23

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  1. Lecture 23 CSE 331 Oct 25, 2017

  2. Graded pitch PAY ATTENTION TO THE COMMENTS

  3. Shortest Path Problem http://xkcd.com/85/

  4. Another more important application Is BGP a known acronym for you? Routing uses shortest path algorithm

  5. Shortest Path problem s s s 100 Input: Directed graph G=(V,E) Edge lengths, le for e in E “start” vertex s in V w w 5 5 5 15 15 u u u Output: All shortest paths from s to all nodes in V

  6. Dijkstra’s shortest path algorithm E. W. Dijkstra (1930-2002)

  7. Dijkstra’s shortest path algorithm 1 d’(w) = min e=(u,w) in E, u in Rd(u)+le 3 3 y 4 u 1 1 1 d(s) = 0 d(u) = 1 4 s x 4 2 d(w) = 2 d(x) = 2 2 2 d(y) = 3 d(z) = 4 2 w z 5 4 3 2 s Input: Directed G=(V,E), le ≥ 0, s in V w u R = {s}, d(s) =0 Shortest paths x While there is a x not in R with (u,x) in E, u in R Pick w that minimizes d’(w) Add w to R z y d(w) = d’(w)

  8. Couple of remarks The Dijkstra’s algo does not explicitly compute the shortest paths Can maintain “shortest path tree” separately Dijkstra’s algorithm does not work with negative weights Left as an exercise

  9. Rest of Today’s agenda Prove the correctness of Dijkstra’s Algorithm Runtime analysis of Dijkstra’s Algorithm

  10. Reading Assignment Sec 4.4 of [KT]

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