Matthias Walter

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Given an undirected graph, the non-empty subgraph polytope is the convex hull of the characteristic vectors of pairs (F, S) where S is a non-empty subset of nodes and F is a subset of the edges with both endnodes in S. We obtain a strong relationship between the non-empty subgraph polytope and the spanning forest polytope. We further show that these(More)
Preface During my internship at the IBM T.J. Watson Research Center in fall 2010 I studied recent papers that may be suitable for an implementation for CPLEX, one of the state-of-the-art optimization suites. The main topic was cutting planes because an implementation was relatively easy to create without requiring specific (and secret) internal information.(More)
We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of matchings, extended by a binary number indicating whether the matching contains two specific edges. This polytope is associated to the quadratic matching problem with a single linearized quadratic term. We provide a complete irredundant inequality description, which(More)
Many of the patients undergoing intradetrusor onabotulinumtoxinA injections for refractory neurogenic detrusor overactivity (NDO) present with chronic bacteriuria. In these patients, antibiotic prophylaxis has been widely recommended since bacteriuria might impair treatment efficacy and cause urinary tract infections (UTI) but the evidence is limited. The(More)
We show that the independence polytope of every regular matroid has an extended formulation of size quadratic in the size of its ground set. This generalizes a similar statement for (co-)graphic matroids, which is a simple consequence of Martin's [9] extended formulation for the spanning-tree polytope. In our construction, we make use of Seymour's(More)
Purpose To examine the value of surveillance urethro-cystoscopy in patients with neurogenic lower urinary tract dysfunction (NLUTD) in regard to the conflicting literature as it is generally agreed that patients with NLUTD are at increased risk for bladder cancer. In a cross-sectional study, a consecutive series of 129 patients (50 females, 79 males, mean(More)