We describe how to use the traveling salesman problem (TSP) to create continuous line drawings of target pictures. CitationDept. of Mathematics, Oberlin College, Oberlin, Ohio 44074ArticleDownload View PDF
We present a new implementation of a widely used swap-based local search procedure for the P-median problem, proposed in 1968 by Teitz and Bart. Our method produces the same output as the best alternatives described in the literature and, even though it does not have a better worst-case complexity, it can be significantly faster in … Read more
In a previous work, we proposed a new integer programming formulation for the graph coloring problem which, to a certain extent, avoids symmetry. We studied the facet structure of the 0/1-polytope associated with it. Based on these theoretical results, we present now a Branch-and-Cut algorithm for the graph coloring problem. Our computational experiences compare favorably … Read more
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional complication that each pair of nodes have an … Read more
Semidefinite Programming (SDP) has recently turned out to be a very powerful tool for approximating some NP-hard problems. The nature of the Quadratic Assignment Problem suggests SDP as a way to derive tractable relaxation. We recall some SDP relaxations of QAP and solve them approximately using the Bundle Method. The computational results demonstrate the efficiency … Read more
Stable multi-sets are an evident generalization of the well-known stable sets. As integer programs, they constitute a general structure which allows for a wide applicability of the results. Moreover, the study of stable multi-sets provides new insights to well-known properties of stable sets. In this paper, we continue our investigations started in Koster and Zymolka … Read more
In this paper, ant colony optimization (ACO) algorithms are proposed for reservoir operation. Through a collection of cooperative agents called ants, the nearoptimum solution to the reservoir operation can be effectively achieved. To apply ACO algorithms, the problem is approached by considering a finite horizon with a time series of inflow, classifying the reservoir volume … Read more
Let $P$ be a combinatorial optimization problem, and let $A$ be an approximation algorithm for $P$. The domination ratio $\domr(A,s)$ is the maximal real $q$ such that the solution $x(I)$ obtained by $A$ for any instance $I$ of $P$ of size $s$ is not worse than at least the fraction $q$ of the feasible solutions … Read more
The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We … Read more
Recently, Aguilera et al.\ exposed a beautiful relationship between antiblocker duality and the lift-and-project operator proposed by Balas et al. We present a very short proof of their result that the \BCC-rank of the clique polytope is invariant under complementation. The proof of Aguilera et al. relies on their main technical result, which describes a … Read more