Lower bounds for sizes of semidefinite formulations for some combinatorial optimization problems

Details Lower bounds for sizes of semidefinite formulations for some combinatorial optimization problems Lower bounds for sizes of semidefinite formulations for some combinatorial optimization problems

2012-03-18

arxiv.org/abs/1203.3961v1

Mathematics

Combinatorics

Abstract, 4 pages

Scientific paper

We present lower bounds for sizes of semidefinite extended formulations for combinatorial optimization problems. Among other things, we prove that the Goemans-Williamson SDP relaxation (of size linear in the number of vertices) for Max-Cut is the smallest possible, whereas any semidefinite extended formulation for Max-Cut which dominates the triangle inequalities of the usual linear formulation has at least quadratic size.

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