Unformatted text preview: CS 473: Algorithms, Fall 2010 HBS 2 Problem 1. [Quick Fix] Your friend suggests that the easiest algorithm for finding shortest paths in a directed graph with negativeweighted edges is to make all the weights positive by adding a sufficiently large constant to each weight and then running Dijkstra’s algorithm. Give an example that you can show your friend to prove that his or her method is incorrect. Problem 2. [Reductions] Show that the following problems can be reduced to the standard shortest path problems. No proof required. • Given directed graph G = ( V,E ) and two disjoint sets of nodes S,T . Find the shortest path from some node in S to some node in T . • G is a directed graph and nodes and edges have nonnegative lengths. Find s t shortest path where the length of a path is equal to the sum of the lengths of the nodes and edges on the path. • Given a directed graph G with node lengths (no edge lengths), is there a negative length cycle? Here the length of a cycle is the sum of the lengths of nodes on the cycle.cycle?...
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 Fall '08
 Chekuri,C
 Algorithms, Graph Theory, Shortest path problem, shortest path, Dijkstra

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