Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
The spatial complexity of oblivious k-probe Hash functions
SIAM Journal on Computing
Journal of the ACM (JACM)
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Constructing extended formulations from reflection relations
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Extended formulations, nonnegative factorizations, and randomized communication protocols
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
An algebraic approach to symmetric extended formulations
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Lifts of Convex Sets and Cone Factorizations
Mathematics of Operations Research
An information complexity approach to extended formulations
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In 1991, Yannakakis [17] proved that no symmetric extended formulation for the matching polytope of the complete graph Kn with n nodes has a number of variables and constraints that is bounded subexponentially in n. Here, symmetric means that the formulation remains invariant under all permutations of the nodes of Kn. It was also conjectured in [17] that “asymmetry does not help much,” but no corresponding result for general extended formulations has been found so far. In this paper we show that for the polytopes associated with the matchings in Kn with $\lfloor\log n\rfloor$ edges there are non-symmetric extended formulations of polynomial size, while nevertheless no symmetric extended formulation of polynomial size exists. We furthermore prove similar statements for the polytopes associated with cycles of length $\lfloor\log n\rfloor$. Thus, with respect to the question for smallest possible extended formulations, in general symmetry requirements may matter a lot.