Fooling sets and the Spanning Tree polytope
نویسندگان
چکیده
منابع مشابه
Fooling Sets and the Spanning Tree Polytope
In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with n nodes. The best known lower bound is Ω(n), the best known upper bound is O(n). In this note we show that the venerable fooling set method cannot be used to improve the l...
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ABSTRACT. An n×n matrix M is called a fooling-set matrix of size n if its diagonal entries are nonzero and Mk,lMl,k = 0 for every k 6= l. Dietzfelbinger, Hromkovič, and Schnitger (1996) showed that n ≤ (rkM)2 , regardless of over which field the rank is computed, and asked whether the exponent on rkM can be improved. We settle this question. In characteristic zero, we construct an infinite fami...
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In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with n nodes. The best known lower bound is the trival (dimension) bound, Ω(n), the best known upper bound is the extended formulation by Wong (1980) of size O(n) (also Martin,...
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ژورنال
عنوان ژورنال: Information Processing Letters
سال: 2018
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2017.05.009