In this paper, we study the k-level facility location problem with outliers (k-LFLPWO), which is an extension of the well-known k-level facility location problem (k-LFLP). In the k-LFLPWO, we are given k facility loca...
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In this paper, we study the k-level facility location problem with outliers (k-LFLPWO), which is an extension of the well-known k-level facility location problem (k-LFLP). In the k-LFLPWO, we are given k facility location sets, a client location set of cardinality n and a non-negative integer q < n. Every facility location set has a different level which belongs to {1, 2,..., k}. For any facility location, there is an opening cost. For any two locations, there is a connecting cost. We wish to connect at least n - q clients to opened facilities from level 1 to level k, such that the total cost including opening costs and connecting costs is minimized. Our main contribution is to present a 6-approximation algorithm, which is based on the technique of primal-dual, for the k-LFLPWO.
Considerable efforts have been dedicated to develop both heuristic and approximation algorithms for the NP-complete delay-constrained least-cost (DCLC) routing problem, but to the best of our knowledge, no prior work ...
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Considerable efforts have been dedicated to develop both heuristic and approximation algorithms for the NP-complete delay-constrained least-cost (DCLC) routing problem, but to the best of our knowledge, no prior work has been done to mingle the two tracks of research. In this letter we introduce a novel idea to show how a heuristic method can be used to boost the average performance of an approximation algorithm. Simulations on networks of up to 8192 nodes demonstrate that our new hybrid epsilon-approximation algorithm is faster than the best known approximation algorithm by one or two orders of magnitude ( depending on the network size and epsilon).
We study the problem of scheduling a single machine with the precedence relation on the set of jobs to minimize average weighted completion time. The problem is strongly NP-hard. The first combinatorial 2-approximatio...
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We study the problem of scheduling a single machine with the precedence relation on the set of jobs to minimize average weighted completion time. The problem is strongly NP-hard. The first combinatorial 2-approximation algorithm for this scheduling problem was developed by the author in 1992 (in fact, this algorithm solves a more general problem). Here we give an efficient implementation of this algorithm and show that its running time is O(nMF(n,m)), where n is the number of jobs, m is the number of arcs in the precedence relation graph, and MF(n,m) denotes the complexity of the maximal flow computation in a network with n nodes and m arcs. Thus, our algorithm is competitive to the best 2-approximation algorithms for this scheduling problem developed starting since 1997. (C) 2003 Published by Elsevier B.V.
We offer the currently best approximation ratio 2.375 for the facility location problem with submodular penalties (FLPSP), improving not only the previous best combinatorial ratio 3, but also the previous best non-com...
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We offer the currently best approximation ratio 2.375 for the facility location problem with submodular penalties (FLPSP), improving not only the previous best combinatorial ratio 3, but also the previous best non-combinatorial ratio 2.488. We achieve this improved ratio by combining the primal-dual scheme with the greedy augmentation technique. (C) 2012 Elsevier B.V. All rights reserved.
The quay crane scheduling problem studied in this article is to determine the handling sequence of ship bays for quay cranes assigned to a container ship considering handling priority of every ship bay. This article p...
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The quay crane scheduling problem studied in this article is to determine the handling sequence of ship bays for quay cranes assigned to a container ship considering handling priority of every ship bay. This article provides a mixed integer programming model for the considered quay crane scheduling problem that is NP-complete in nature. An approximation algorithm is proposed to obtain near optimal solutions and a worst-case analysis for the approximation algorithm is performed. Computational experiments are conducted to examine the proposed model and solution algorithm. The computational results show that the proposed approximation algorithm is effective and efficient in solving the considered quay crane scheduling problem.
This paper presents an improved lower bound and an approximation algorithm based on spectral decomposition for the binary constrained quadratic programming problem. To decompose spectrally the quadratic matrix in the ...
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This paper presents an improved lower bound and an approximation algorithm based on spectral decomposition for the binary constrained quadratic programming problem. To decompose spectrally the quadratic matrix in the objective function, we construct a low rank problem that provides a lower bound. Then an approximation algorithm for the binary quadratic programming problem together with a worst case performance analysis for the algorithm is provided.
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.
The problem of finding a largest stable matching where preference lists may include ties and unacceptable partners (MAX SMTI) is known to be NP-hard. It cannot be approximated within 33/29 (> 1.1379) unless P=NP, a...
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The problem of finding a largest stable matching where preference lists may include ties and unacceptable partners (MAX SMTI) is known to be NP-hard. It cannot be approximated within 33/29 (> 1.1379) unless P=NP, and the current best approximation algorithm achieves the ratio of 1.5. MAX SMTI remains NP-hard even when preference lists of one side do not contain ties, and it cannot be approximated within 21/19 (> 1.1052) unless P=NP. However, even under this restriction, the best known approximation ratio is still 1.5. In this paper, we improve it to 25/17 (< 1.4706).
In the k-means problem with penalties, we are given a data set D subset of R-l of n points where each point j is an element of D is associated with a penalty cost p(j) and an integer k. The goal is to choose a set CS ...
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In the k-means problem with penalties, we are given a data set D subset of R-l of n points where each point j is an element of D is associated with a penalty cost p(j) and an integer k. The goal is to choose a set CS subset of R-l with vertical bar CS vertical bar <= k and a penalized subset D-p subset of D to minimize the sum of the total squared distance from the points in D\D-p to CS and the total penalty cost of points in D-p, namely Sigma(j is an element of D\Dp) d(2)(j, CS)+ Sigma(j is an element of Dp) p(j). We employ the primaldual technique to give a pseudo-polynomial time algorithm with an approximation ratio of (6.357+ epsilon) for the k-means problem with penalties, improving the previous best approximation ratio 19.849 + epsilon for this problem given by Feng et al. in Proceedings of FAW(2019).
We study a natural extension of the classical traveling salesman problem (TSP) in the situation where multiple salesmen are dispatched from a number of different depots. As with the TSP, this problem is motivated by a...
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We study a natural extension of the classical traveling salesman problem (TSP) in the situation where multiple salesmen are dispatched from a number of different depots. As with the TSP, this problem is motivated by a large range of applications in vehicle routing. Although it is known to have a 2-approximation algorithm, whether the problem has a 3/2-approximation algorithm, as is the case with the well-known Christofides heuristic for the TSP, remains an open question. We answer this question positively by providing a 3/2-approximation algorithm for the problem with a fixed number of depots. The algorithm uses an edge exchange strategy, and its analysis hinges on a newly discovered exchange property of matroids. In addition, the algorithm is applied to multidepot extensions of other TSP variants, and we show for the first time, to our knowledge, that for these multidepot extensions the same best constant approximation ratios can be achieved as for their respective single-depot cases.
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