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Unformatted text preview: CS231: Topics in Combinatorial Algorithms Prof. Suri Homework Assignment 1 Handed Out: Sept 28 Due: Oct 7 1. Let G = ( V,E ) be a directed graph whose edges have real-valued costs (possibly negative). We call G loop-free if it contains no directed loop (cycle). Describe an O ( m ) worst-case time algorithm for computing a shortest path from a source node s to a destination d in a loop-free graph, where m is the number of edges in G . Be sure to analyze the time complexity, prove its correctness, and argue that the algorithm works for negative edge costs as well. 2. Occasionally in a shortest path problem, multiple and possibly conflicting, criteria for the quality may be applicable. For instance, each link may be associated with both a cost (money) and latency (delay). In this problem, we consider two possible formulations to deal with such situations. Let G = ( V,E ) be a directed graph, each of whose edges e is associated with a non-negative cost ( e ) as well as a non-negative length...
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- Fall '09
- Graph Theory, Computational complexity theory, Shortest path problem, Prof. Suri, Combinatorial Algorithms