Lecture 24 CSE 331 Oct 24, 2014.

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Presentation transcript:

Lecture 24 CSE 331 Oct 24, 2014

Graded Mid-terms Will be handed out at the end of the lecture Posts with solutions/grading details over the weekend Will assign a temp letter grade over the weekend

HW stuff Delay in handing out graded HW 5 HW 6 posted on piazza

Mini Project report Due Nov 5

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

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

Dijkstra’s shortest path algorithm 1 d’(w) = min e=(u,w) in E, u in R d(u)+le 1 2 4 3 y 4 3 u d(s) = 0 d(u) = 1 s x 2 4 d(w) = 2 d(x) = 2 d(y) = 3 d(z) = 4 w z 5 4 2 s w Input: Directed G=(V,E), le ≥ 0, s in V 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 z y Pick w that minimizes d’(w) Add w to R d(w) = d’(w)

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

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

Reading Assignment Sec 4.4 of [KT]