Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the extended formulation also depends on the number of rows of the slack matrix (hence, of the exact description in the original space). We give general sufficient conditions under which those tools can be implemented as to be output-efficient, showing applications to e.g. Yannakakis' extended formulation for the stable set polytope of perfect graphs, for which, to the best of our knowledge, an efficient construction was previously not known. For specific classes of polytopes, we give also a direct, efficient construction of those extended formulations. Finally, we deal with extended formulations coming from certain unambiguous non-deterministic protocols.

Extended Formulations from Communication Protocols in Output-Efficient Time

Aprile, M;
2019

Abstract

Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the extended formulation also depends on the number of rows of the slack matrix (hence, of the exact description in the original space). We give general sufficient conditions under which those tools can be implemented as to be output-efficient, showing applications to e.g. Yannakakis' extended formulation for the stable set polytope of perfect graphs, for which, to the best of our knowledge, an efficient construction was previously not known. For specific classes of polytopes, we give also a direct, efficient construction of those extended formulations. Finally, we deal with extended formulations coming from certain unambiguous non-deterministic protocols.
2019
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019
978-3-030-17952-6
978-3-030-17953-3
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3476521
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