We present a -approximation algorithm for the non-uniform soft capacitated k-facility location problem, violating the capacitated constrains by no more than a factor of 25. The main technique is based on the primal-du...
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We present a -approximation algorithm for the non-uniform soft capacitated k-facility location problem, violating the capacitated constrains by no more than a factor of 25. The main technique is based on the primal-dual algorithm for the soft capacitated facility location problem, and the exploitation of the combinatorial structure of the fractional solution for the soft capacitated k-facility location problem.
In this paper, we introduce a squared metric k-facility location problem (SM-k-FLP) which is a generalization of the squared metric facility location problem and k-facility location problem (k-FLP). In the SM-k-FLP, w...
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In this paper, we introduce a squared metric k-facility location problem (SM-k-FLP) which is a generalization of the squared metric facility location problem and k-facility location problem (k-FLP). In the SM-k-FLP, we are given a client set and a facility set from a metric space, a facility opening cost for each , and an integer k. The goal is to open a facility subset with and to connect each client to the nearest open facility such that the total cost (including facility opening cost and the sum of squares of distances) is minimized. Using local search and scaling techniques, we offer a constant approximation algorithm for the SM-k-FLP.
Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known ...
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Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known algorithms in several ways, including adding randomization and applying sparsification as a preprocessing step. The latter improvement produces the first LP for this problem with bounded integrality gap. The new algorithm obtains an approximation factor of 17.46. We also give a 3.05 approximation with small budget violation.
We present a (1 + root 3 + is an element of)-approximation algorithm for the k-median problem with uniform penalties, extending the recent result by Li and Svensson for the classical k-median problem without penalties...
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We present a (1 + root 3 + is an element of)-approximation algorithm for the k-median problem with uniform penalties, extending the recent result by Li and Svensson for the classical k-median problem without penalties. One important difference of this work from that of Li and Svensson is a new definition of sparse instance to exploit the combinatorial structure of our problem. (C) 2018 Elsevier B.V. All rights reserved.
We study a multiple-vehicle routing problem with a minimum makespan objective and compatibility constraints. We provide an approximation algorithm and a nearly-matching hardness of approximation result. We also provid...
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We study a multiple-vehicle routing problem with a minimum makespan objective and compatibility constraints. We provide an approximation algorithm and a nearly-matching hardness of approximation result. We also provide computational results on benchmark instances with diverse sizes showing that the proposed algorithm (i) has a good empirical approximation factor. (ii) runs in a short amount of time and (iii) produces solutions comparable to the best feasible solutions found by a direct integer program formulation. (C) 2018 Elsevier 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.
For two sequences P and Q of n points in R-d, we compute an approximation to the discrete Frechet distance. Our f-approximation algorithm runs in time O(n logn + n(2)/f(2)), for any f is an element of[1, root n/log n]...
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For two sequences P and Q of n points in R-d, we compute an approximation to the discrete Frechet distance. Our f-approximation algorithm runs in time O(n logn + n(2)/f(2)), for any f is an element of[1, root n/log n] and d = O(1), which improves (and, at the same time, slightly simplifies) the previous O(n logn + n(2)/f)-time algorithm by Bringmann and Mulzer [SoCG'15]. (C) 2018 Elsevier B.V. All rights reserved.
When facilities are built to serve end consumers directly, it is natural that consumer demands are affected by the number of open facilities. Moreover, sometimes a facility becomes more attractive if other facilities ...
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When facilities are built to serve end consumers directly, it is natural that consumer demands are affected by the number of open facilities. Moreover, sometimes a facility becomes more attractive if other facilities around it are built. To capture these factors, in this study we construct a discrete location model for profit maximization with endogenous consumer demands and network effects. The effective demand is then a concave function of the sum of benefits of open facilities due to the diminishing marginal benefit effect. When the function is linear, we design a polynomial-time algorithm to find an optimal solution. When it is nonlinear, we show that the problem is NP-hard and develop an approximation algorithm based on demand function approximation, linear relaxation, decomposition, and sorting. It is demonstrated that the proposed algorithm has worst-case performance guarantees for some special cases of our problem. Numerical studies are conducted to demonstrate the average performance and general applicability of our algorithms. (C) 2017 Elsevier B.V. All rights reserved.
In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone ...
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In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). In this paper, we present a constant approximation algorithm for the minimum weight (k, m)-CDS problem in unit disk graphs under the assumption that k and m are two fixed constants with m >= k. Prior to this paper, constant approximation algorithms are known for k = 1 with weight and 2 <= k <= 3 without weight. Our result is the first constant approximation algorithm for the (k, m)-CDS problem with general k, m and with weight. The performance ratio is (alpha+5 rho) for k >= 3 and (alpha+2.5 rho) for k = 2, where a is the performance ratio for the minimum weight m-fold dominating set problem and. is the performance ratio for the subset k-connected subgraph problem (both problems are known to have constant performance ratios).
An l-pseudoforest is a graph each of whose connected component is at most l edges away from being a tree. The l-Pseudoforest Deletion problem is to delete a vertex set P of minimum weight from a given vertex-weighted ...
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ISBN:
(纸本)9783319947761;9783319947754
An l-pseudoforest is a graph each of whose connected component is at most l edges away from being a tree. The l-Pseudoforest Deletion problem is to delete a vertex set P of minimum weight from a given vertex-weighted graph G = (V, E) such that the remaining graph G[V \ P] is an l-pseudoforest. The Feedback Vertex Set problem is a special case of the l-Pseudoforest Deletion problem with l = 0. In this paper, we present a polynomial time 4l-approximation algorithm for the l-Pseudoforest Deletion problem with l >= 1 by using the local ratio technique. When l = 1, we get a better approximation ratio 2 for the problem by further analyzing the algorithm, which matches the current best constant approximation factor for the Feedback Vertex Set problem.
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