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CPAIOR
2009
Springer

Backdoors to Combinatorial Optimization: Feasibility and Optimality

9 years 10 months ago
Backdoors to Combinatorial Optimization: Feasibility and Optimality
There has been considerable interest in the identification of structural properties of combinatorial problems that lead, directly or indirectly, to the development of efficient algorithms for solving them. One such concept is that of a backdoor set—a set of variables such that once they are instantiated, the remaining problem simplifies to a tractable form. While backdoor sets were originally defined to capture structure in decision problems with discrete variables, here we introduce a notion of backdoors that captures structure in optimization problems, which often have both discrete and continuous variables. We show that finding a feasible solution and proving optimality are characterized by backdoors of different kinds and size. Surprisingly, in certain mixed integer programming problems, proving optimality involves a smaller backdoor set than finding the optimal solution. We also show extensive results on the number of backdoors of various sizes in optimization problems. Ov...
Bistra N. Dilkina, Carla P. Gomes, Yuri Malitsky,
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CPAIOR
Authors Bistra N. Dilkina, Carla P. Gomes, Yuri Malitsky, Ashish Sabharwal, Meinolf Sellmann
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