The semidefinite programming formulation of the Lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number and the clique number of a graph, but also leads to heuristics for graph coloring and extracting large cliques. This semidefinite programming formulation can be tightened toward either number by adding … Read more
In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of … Read more
Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. We formulate this as a combinatorial linear program and give … Read more
In power law graphs, cut quality varies inversely with cut balance. Using some million node social graphs as a test bed, we empirically investigate this property and its implications for graph partitioning. We use six algorithms, including Metis and MQI (state of the art methods for finding bisections and quotient cuts) and four relaxation/rounding methods. … Read more
Level of Repair Analysis (LORA) is a prescribed procedure for defence logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize … Read more
A set $S$ of vertices in a digraph $D=(V,A)$ is a kernel if $S$ is independent and every vertex in $V-S$ has an out-neighbor in $S$. We show that there exist $O(n2^{19.1 \sqrt{k}}+n^4)$-time and $O(2^{19.1 \sqrt{k}} k^9 + n^2)$-time algorithms for checking whether a planar digraph $D$ of order $n$ has a kernel with at … Read more
We propose a new strategy for solving the non-bijective graph matching problem in model-based pattern recognition. The search for the best correspondence between a model and an over-segmented image is formulated as a combinatorial optimization problem, defined by the relational attributed graphs representing the model and the image where recognition has to be performed, together … Read more
We show in this work how the problem of routing and wavelength assignment in all-optical networks may be solved by a combined approach involving the computation of alternative routes for the lightpaths, followed by the solution of a partition coloring problem in a conflict graph. A new tabu search heuristic is also proposed for the … Read more
We describe a graph coloring problem associated with the determination of mathematical derivatives. The coloring instances are obtained as intersection graphs of row partitioned sparse derivative matrices. The size of the graph is dependent on the partition and can be varied between the number of columns and the number of nonzero entries. If solved exactly … Read more
A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of … Read more