The k-Level Concentrator Location Problem is a variant of the k-Level Facility Location Problem, where in contrast to the classical model, service costs are charged only once and not proportional to the demand. We pre...
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The k-Level Concentrator Location Problem is a variant of the k-Level Facility Location Problem, where in contrast to the classical model, service costs are charged only once and not proportional to the demand. We present a new approximation algorithm with a performance guarantee of 3/2(3(k) - 1), improving over the 1.52 . 9(k-1)-approximation algorithm proposed by Kantor and Peleg. Moreover, the analysis is considerably shortened by using complementary slackness conditions. (C) 2011 Elsevier B.V. All rights reserved.
We introduce the vertex cover P-n (VCPn) problem, that is, the problem of finding a minimum weight set F subset of V such that the graph G[V - F] has no P-n, where P-n is a path with n vertices. The problem also has i...
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We introduce the vertex cover P-n (VCPn) problem, that is, the problem of finding a minimum weight set F subset of V such that the graph G[V - F] has no P-n, where P-n is a path with n vertices. The problem also has its application background. In this paper, we first show that the VCPn problem is NP-hard for any integer n >= 2. Then we restrict our attention to the VCP3 problem and give a 2-approximation algorithm using the primal-dual method. (C) 2011 Elsevier B.V. All rights reserved.
We developed a new practical optimization method that gives approximate solutions for large-scale real instances of the Uncapacitated Facility Location Problem. The optimization consists of two steps: application of t...
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We developed a new practical optimization method that gives approximate solutions for large-scale real instances of the Uncapacitated Facility Location Problem. The optimization consists of two steps: application of the Greedy-Interchange heuristic using a small subset of warehouse candidates, and application of the newly developed heuristic named Balloon Search that takes account of all warehouse candidates, and runs in O(3n + 2n log n) expected time (n is the number of nodes of the underlying graph). Our experiments on the spare parts logistics of a Japanese manufacturing company with 6000 customers and 380,000 warehouse candidates led us to conclude that the Greedy heuristic improved the total cost by 9%-11%, that the Interchange heuristic improved the total cost by an additional 0.5%-1.5%, and that Balloon Search improved it by a further 0.5%-1.5%.
We present a polynomial-time algorithm approximating the minimum weight edge dominating set problem within a factor of 2. It has been known that the problem is NP-hard but, when edge weights are uniform (so that the s...
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We present a polynomial-time algorithm approximating the minimum weight edge dominating set problem within a factor of 2. It has been known that the problem is NP-hard but, when edge weights are uniform (so that the smaller the better), it can be efficiently approximated within a factor of 2. When general weights were allowed, however, very little had been known about its approximability, and only very recently was it shown to be approximable within a factor of 2 1/10 by reducing to the edge cover problem via LP relaxation. In this paper we extend the approach given therein, by studying more carefully polyhedral structures of the problem, and obtain an improved approximation bound as a result. While the problem considered is as hard to approximate as the weighted vertex cover problem is, the best approximation (constant) factor known for vertex cover is 2 even for the unweighted case, and has not been improved in a long time, indicating that improving our result would be quite difficult. (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper, we consider an extension of the classical facility location problem, namely k-facility location problem with linear penalties. In contrast to the classical facility location problem, this problem opens ...
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In this paper, we consider an extension of the classical facility location problem, namely k-facility location problem with linear penalties. In contrast to the classical facility location problem, this problem opens no more than k facilities and pays a penalty cost for any non-served client. We present a local search algorithm for this problem with a similar but more technical analysis due to the extra penalty cost, compared to that in Zhang (Theoretical Computer Science 384:126-135, 2007). We show that the approximation ratio of the local search algorithm is , where is a parameter of the algorithm and is a positive number.
Cloud providers face the challenge of efficiently managing their infrastructure through minimizing resource consumption while allocating service requests such that their revenue is maximized. Solutions addressing this...
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Cloud providers face the challenge of efficiently managing their infrastructure through minimizing resource consumption while allocating service requests such that their revenue is maximized. Solutions addressing this challenge should consider the sharing of memory pages among virtual machines (VMs) and the available capacity of each type of requested resources. We provide such solution by designing a greedy approximation algorithm for solving the sharing-aware virtual machine revenue maximization (SAVMRM) problem. The SAVMRM problem requires determining the set of VMs that can be instantiated on a given server such that the revenue derived from hosting the VMs is maximized. In addition, we model the SAVMRM problem as a multilinear binary program and optimally solve it, while accounting for page sharing and multiple resource constraints. We determine and analyze the approximability properties of our proposed greedy algorithm and evaluate it by performing extensive experiments using Google cluster workload traces. The experimental results show that under various scenarios, our proposed algorithm generates higher revenue than other VM allocation algorithms while achieving significant reduction of allocated memory.
The classical seriation problem consists in finding a permutation of the rows and the columns of the distance (or, more generally, dissimilarity) matrix d on a finite set X so that small values should be concentrated ...
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The classical seriation problem consists in finding a permutation of the rows and the columns of the distance (or, more generally, dissimilarity) matrix d on a finite set X so that small values should be concentrated around the main diagonal as close as possible, whereas large values should fall as far from it as possible. This goal is best achieved by considering the Robinson property: a distance d (R) on X is Robinsonian if its matrix can be symmetrically permuted so that its elements do not decrease when moving away from the main diagonal along any row or column. If the distance d fails to satisfy the Robinson property, then we are lead to the problem of finding a reordering of d which is as close as possible to a Robinsonian distance. In this paper, we present a factor 16 approximation algorithm for the following NP-hard fitting problem: given a finite set X and a dissimilarity d on X, we wish to find a Robinsonian dissimilarity d (R) on X minimizing the l (a)-error aEuro-d-d (R) aEuro-(a)=max (x,yaX) {vertical bar d(x,y)-d (R) (x,y)vertical bar} between d and d (R) .
We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity can be split into a bounded number k (i) of equally-sized chunks that can be routed on diff...
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We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity can be split into a bounded number k (i) of equally-sized chunks that can be routed on different paths. We show that in contrast to the single-commodity case this problem is NP-hard, and hard to approximate to within a factor of alpha > 1/2. We present a polynomial time 1/2-approximation algorithm for the case of uniform chunk size over both commodities and show that for even k (i) and a mild cut condition it can be modified to yield an exact method. The uniform case can be used to derive a 1/4-approximation for the maximum concurrent (k (1), k (2))-splittable flow without chunk size restrictions for fixed demand ratios.
We study the multiple Hamiltonian path problem (MHPP) defined on a complete undirected graph G with n vertices. The edge weights of G are non-negative and satisfy the triangle inequality. The MHPP seeks to find a coll...
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We study the multiple Hamiltonian path problem (MHPP) defined on a complete undirected graph G with n vertices. The edge weights of G are non-negative and satisfy the triangle inequality. The MHPP seeks to find a collection of k paths with exactly one visit to each vertex of G with the minimum total edge weight, where endpoints of the paths are not prefixed. We present a 3/2-approximation algorithm for MHPP with time complexity O (n3) for arbitrary k > 1.& COPY;2023 Elsevier B.V. All rights reserved.
We consider the k-level stochastic facility location problem. For this, we present an LP rounding algorithm that is 3-approximate. This result is achieved by a novel integer linear programming formulation that exploit...
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We consider the k-level stochastic facility location problem. For this, we present an LP rounding algorithm that is 3-approximate. This result is achieved by a novel integer linear programming formulation that exploits the stochastic structure. (C) 2010 Elsevier B.V. All rights reserved.
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