70 research outputs found
Approximation algorithms for rectangle stabbing and interval stabbing problems.
Full text linkInthe weighted rectangle stabbing problem we are given a grid in R2 consisting of columns and rows each having a positive integral weight, and a set of closed axis-parallel rectangles each having a positive integral demand. The rectangles are placed arbitrarily in the grid with the only assumption that each rectangle is intersected by at least one column and at least one row. The objective is to find a minimum-weight (multi)set of columns and rows of the grid so that for each rectangle the total multiplicity of selected columns and rows stabbing it is at least its demand. A special case of this problem arises when each rectangle is intersected by exactly one row. We describe two algorithms, called STAB and ROUND, that are shown to be constant-factor approximation algorithms for different variants of this stabbing problem.Research; Approximation; Algorithms; Problems; Demand;
The three-dimensional matching problem in Kalmanson matrices
Full text linkWe investigate the computational complexity of several special cases of the three-dimensional matching problem where the costs are decomposable and determined by a so-called Kalmanson matrix. For the minimization version we develop an efficient polynomial time algorithm that is based on dynamic programming. For the maximization version, we show that there is a universally optimal matching (whose structure is independent of the particular Kalmanson matrix).Sergey Polyakovskiy, Frits C. R. Spieksma, Gerhard J. Woeginge
Local search heuristics for multi-index assignment problems with decomposable costs.
Full text linkThe multi-index assignment problem (MIAP) with decomposable costs is a natural generalization of the well-known assignment problem. Applications of the MIAP arise for instance in the field of multi-target multi-sensor tracking. We describe an (exponentially sized) neighborhood for a solution of the MIAP with decomposable costs, and show that one can find a best solution in this neighborhood in polynomial time. Based on this neighborhood, we propose a local search algorithm. We empirically test the performance of published constructive heuristics and the local search algorithm on random instances; a straightforward tabu search is also tested. Finally, we compute lower bounds to our problem, which enable us to assess the quality of the solutions found.Assignment; Costs; Heuristics; Problems; Applications; Performance;
Matrix bids in combinatorial auctions: expressiveness and micro-economic properties
Full text linkA combinatorial auction is an auction where multiple items are for sale simultaneously to a set of buyers. Furthermore, buyers are allowed to place bids on subsets of the available items. This paper focuses on a combinatorial auction where a bidder can express his preferences by means of a so-called ordered matrix bid. Ordered matrix bids are a bidding language that allows a compact representation of a bidder''s preferences, and was developed by Day (2004). We give an overview of how a combinatorial auction with matrix bids works. We elaborate on the relevance of the matrix bid auction and we develop methods to verify whether a given matrix bid satisfies properties related to micro-economic theory as free disposal, subadditivity, submodularity and the gross substitutes property. Finally, we investigate how a collection of arbitrary bids can be represented as a matrix bid.microeconomics ;
The selection of clients for promotion campaigns by means of mathematical programming.
Full text linkA note on a motion control problem for a placement machine.
Full text linkAssembling printed circuit boards effciently using automated placement machines is a challenging task. Here, we focus on a motion control problem for a specific type of placement machines. More specifically,the problem is to establish movement patterns for the robot arm, the feeder rack,and -when appropriate- the work table, of a sequential, pick-and-place machine. In this note we show that a (popular) greedy strategy may not always yield an optimum solution. However, under the Tchebychev metric, as well as under the Manhattan metric, we can model the problem as a linear program, thereby establishing the existence of a polynomial time algorithm for this motion control problem. Finally, we give experimental evidence that computing optimal solutions to this motion control problem can yield significantly better solutions than those found by a greedy method.Algorithms; Computational complexity; Control; Printed circuit boards;
Scheduling with safety distances
No full textWe investigate the problem of Scheduling with Safety Distances (SSD) that consists in scheduling jobs on two parallel machines without machine idle time. Every job is already assigned to its machine, and we just have to specify an ordering of the jobs for each machine. The goal is to find orderings of the jobs such that the minimum time elapsed between any two job completion times is maximized. We prove that this problem is NP-hard in general and give polynomial time algorithms for special cases. These results combined establish a sharp borderline between NP-complete and polynomial solvable versions of the problem SSD
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