Tight extended formulations for independent set∗
نویسندگان
چکیده
This paper describes tight extended formulations for independent set. The first formulation is for arbitrary independence systems and has size O(n+ μ), where μ denotes the number of inclusion-wise maximal independent sets. Consequently, the extension complexity of the independent set polytope of graphs is O(1.4423). The size O(2n) of the second extended formulation depends on the treewidth tw of the graph, which is a common measure of how tree-like it is. This improves upon the size O(n) extended formulations implied by the Sherali-Adams reformulation procedure (as shown by Bienstock and Ozbay). This implies size O(n) extended formulations for outerplanar, series-parallel, and Halin graphs; size 2 √ n) extended formulations for planar graphs; and size O(1.2247) extended formulations for graphs of maximum degree three.
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