We show algorithms for computing representative families matroid intersections and use them in fixed-parameter set packing, covering, facility location problems with multiple constraints. complement our tractability results by hardness results.

This paper seeks to evaluate the performance of genetic algorithms (GA) as an alternative procedure for generating optimal or near-optimal solutions for location problems. The specific problems considered are the uncapacitated and capacitated fixed charge problems, the maximum covering problem, and competitive location models. We compare the performance of the GA-based heuristics developed agai...

We present approximation algorithms with O(n) processing time for the minimum vertex and edge guard problems in simple polygons. It is improved from previous O(n) time algorithms of Ghosh. For simple polygon, there are O(n) visibility regions, thus any approximation algorithm for the set covering problem with approximation ratio of log(n) can be used for the approximation of n vertex and edge g...

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed component f , and a variable component b that is proportional to the field-of-view area. When only one type of sensor or, in general, one type of disc, is availa...

The interest in collaborative logistics is fuelled by the ever increasing pressure on companies to operate more efficiently, the realization that suppliers, consumers, and even competitors, can be potential collaborative partners in logistics, and the connectivity provided by the Internet. Logistics exchanges or collaborative logistics networks use the Internet as a common computing platform to...

In this paper we identify various inaccuracies in the paper by R. R. Saxena and S. R. Arora, A Linearization technique for solving the Quadratic Set Covering Problem, Optimization, 39 (1997) 33-42. In particular, we observe that their algorithm does not guarantee optimality, contrary to what is claimed. Experimental analysis has been carried out to assess the value of this algorithm as a heuris...

We present a new Lagrangian-based heuristic for solving large-scale set-covering problems arising from crew-scheduling at the Italian Railways (Ferrovie dello Stato). Our heuristic obtained impressive results when compared to state of the art codes on a test-bed provided by the company, which includes instances with sizes ranging from 50,000 variables and 500 constraints to 1,000,000 variables ...

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit simplex. Such setting yields precise asymptotic characterization in the high-rate regime. Our main contribution is a simple and asymptotically optimal algorithm fo...

This paper investigates the semi-online machine covering problems on m ≥ 3 parallel identical machines. Three different semi-online versions are studied and optimal algorithms are proposed. We prove that if the total processing time of all jobs or the largest processing time of all jobs is known in advance, the competitive ratios of the optimal algorithms are both m − 1. If the total processing...

The disc covering problem asks to cover a set of points on the plane with a minimum number of fix-sized discs. We develop an O(n(log n)(log log n)) deterministic time 2.8334-approximation algorithm for this problem. Previous approximation algorithms [7, 3, 6], when used to achieve the same approximation ratio for the disc covering problem, will have much higher time complexity than our algorithms.