Fooling sets and the Spanning Tree polytope

  title={Fooling sets and the Spanning Tree polytope},
  author={Kaveh Khoshkhah and Dirk Oliver Theis},
  journal={Inf. Process. Lett.},

On the Combinatorial Lower Bound for the Extension Complexity of the Spanning Tree Polytope

On some problems related to 2-level polytopes

This thesis investigates a number of problems related to 2-level polytopes, in particular regarding their combinatorial structure and extension complexity, and gives an output-efficient algorithm to write down extended formulations for the stable set polytope of perfect graphs.

The Rectangle Covering Number of Random Boolean Matrices

The rectangle covering number of an $n$-by-$n$ Boolean matrix $M$ is the smallest number of 1-rectangles which are needed to cover all the 1-entries of $M$. Its binary logarithm is the

Extension Complexity of Stable Set Polytopes of Bipartite Graphs

This paper proves that the lower bound of the extension complexity of a polytope P is \(\varOmega (n \log n)\) when G is the incidence graph of a finite projective plane and the upper bound is \(O(\frac{n^2}{\log n})\), which is an improvement when G has quadratically many edges.



Smaller Extended Formulations for the Spanning Tree Polytope of Bounded-Genus Graphs

An O(n2+gn)-size extended formulation for the spanning tree polytope of an n-vertex graph embedded in a surface of genus g is given.

Extended Formulations for Combinatorial Polytopes

i Abstract Typically polytopes arising from real world problems have a lot of facets. In some cases even no linear descriptions for them are known. On the other hand many of these polytopes can be

Fooling-sets and rank

Fooling-sets and rank in nonzero characteristic

Dietzfel-binger, Hromkovic, 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.

Extended formulations in combinatorial optimization

This survey presents compact extended formulations for several graph problems involving cuts, trees, cycles and matchings, and for the mixing set, and presents the proof of Fiorini, Massar, Pokutta, Tiwary and de Wolf of an exponential lower bound for the cut polytope.

The (Minimum) Rank of Typical Fooling-Set Matrices

An $\Omega(n)$ bound is proved for the cases when: (a) p tends to 0 quickly enough, (b)p tends to $0$ slowly, and (c) $p\in(0,1]$ is a constant.

Limitations of convex programming: lower bounds on extended formulations and factorization ranks (Dagstuhl Seminar 15082)

This report documents the program and the outcomes of Dagstuhl Seminar 15082 "Limitations of convex programming: lower bounds on extended formulations and factorization ranks" held in February 2015.