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Unformatted text preview: CMSC 451: Shortest Paths with Negative Weights Slides By: Carl Kingsford Department of Computer Science University of Maryland, College Park Based on Section 6.8 of Algorithm Design by Kleinberg & Tardos. Dynamic Programming Principles, Reviewed Dynamic Programming Pattern: 1 Decompose the problem into subproblems. 2 Recursively define the value of a solution of a subproblem by the value of solutions of smaller subproblems. 3 Compute the value of the solutions for subproblems from smaller to larger. 4 Use the choices made (arrows) to reconstruct an actual solution. DP Principles, 2 Principle of Optimality: A problem obeys this principle if an optimal solution to the problem contains within it optimal solutions to subproblems. • Solution to the problem requires making a choice e.g. include the last interval or not? • This choice leaves 1 or more subproblems unsolved. • Assuming you’re given the optimal solution to these subproblems, you show how to construct the optimal solution to the larger subproblem. Shortest Path Problem...
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 Fall '07
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 Graph Theory, Shortest path problem, optimal solution, subproblems, OPT

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