A fooling-set matrix is a square matrix with nonzero diagonal, but at least one in every pair of diagonally opposite entries is 0. Dietzfelbinger et al. ’96 proved that the rank of such a matrix is at least $\sqrt n$, for a matrix of order $n$. We ask for the typical minimum rank of a … Read more
We study the Partition Coloring Problem (PCP), a generalization of the Vertex Coloring Problem where the vertex set is partitioned. The PCP asks to select one vertex for each subset of the partition in such a way that the chromatic number of the induced graph is minimum. We propose a new Integer Linear Programming formulation … Read more
A proper edge-coloring of a given undirected graph with natural numbers identified with colors is an interval (or consecutive) coloring if the colors of edges incident to each vertex form an interval of consecutive integers. Not all graphs admit such an edge-coloring and the problem of deciding whether a graph is interval colorable is NP-complete. … Read more
Recently, Buchheim and Klein suggested to study polynomial-time solvable optimisation problems with linear objective functions combined with exactly one additional quadratic monomial. They concentrated on special quadratic spanning tree or forest problems. We extend their results to general matroid optimisation problems with a set of nested monomials in the objective function. The monomials are linearised … Read more
In this paper, we introduce an $O(nm)$ time algorithm to determine the minimum length directed cycle in a directed network with $n$ nodes and $m$ arcs and with no negative length directed cycles. This result improves upon the previous best time bound of $O(nm + n^2 \log\log n)$. Our algorithm first determines the cycle with … Read more
Local graph clustering methods aim to identify well-connected clusters around a given “seed set” of reference nodes. The main focus of prior theoretical work has been on worst-case running time properties or on implicit statistical regularization; and the focus of prior empirical work has been to identify structure in large social and information networks. Here, … Read more
In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify … Read more
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms involve contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing and mean field methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover … Read more
In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set … Read more
This paper proposes a new lower bounding procedure for the Uncapacitated Single Allocation p-Hub Median Problem based on Lagrangean relaxation. For solving the resulting Lagrangean subproblem, the given problem structure is exploited: it can be decomposed into smaller subproblems that can be solved efficiently by combinatorial algorithms. Our computational experiments for some benchmark instances demonstrate … Read more