Integer Programming: Optimization and Evaluation Are Equivalent
James B. Orlin,Abraham P. Punnen,Andreas S. Schulz +2 more
- 24 Jul 2009
- pp 519-529
TL;DR: The results imply that PLS-complete problems cannot have "near-exact" neighborhoods, unless PLS = P, and that optimization and augmentation are equivalent for 0/1-integer programs.
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Abstract: We show that if one can find the optimal value of an integer linear programming problem in polynomial time, then one can find an optimal solution in polynomial time. We also present a proper generalization to (general) integer programs and to local search problems of the well-known result that optimization and augmentation are equivalent for 0/1-integer programs. Among other things, our results imply that PLS-complete problems cannot have "near-exact" neighborhoods, unless PLS = P.
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Citations
Average value of solutions for the bipartite boolean quadratic programs and rounding algorithms
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- 19 Aug 2013
TL;DR: For the bipartite boolean quadratic programming problem (BBQP) with m+n variables, an O(mn) algorithm is given to compute the average objective function value of all solutions where as computing the median objective functionvalue is shown to be NP-hard.
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A Generalized Simplex Method for Integer Problems Given by Verification Oracles
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