spneg - Shortest paths in graphs with negative edge weights...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Shortest paths in graphs with negative edge weights • Let G = ( V,E ) be a directed graph with edge weights c uv for each edge ( u,v ) ∈ E . • Let | V | = n and | E | = m . • Cost c ( p ) of a path p = ( v ,v 1 ,...,v k ) is ∑ k i =1 c v i- 1 ,v i . • Shortest path from s to t is a path with minimum cost among all paths from s to t . • Problem: find a shortest path from s to all vertices. • Need the following fact: – FACT 1: If G has no negative cycles then there is a shortest path from s to t with at most n- 1 edges. 1 Bellman-Ford Algorithm • Works in the presence of negative weight edges but no negative cycles. • Let opt ( i,v ) be the minimum cost of a path from v to t using at most i edges. • To compute opt ( n- 1 ,s ). • Let P be an optimal path with cost opt ( i,v ). • There are two mutually exclusive cases: – CASE 1: P uses at most i- 1 edges: * opt ( i,v ) = opt ( i- 1 ,v )....
View Full Document

This note was uploaded on 02/18/2010 for the course CSB 1208204834 taught by Professor N/a during the Spring '10 term at École Normale Supérieure.

Page1 / 4

spneg - Shortest paths in graphs with negative edge weights...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online