Two on-line algorithms for variable-size and variable-cost bin packing problems are *** first algo- rithm,based on the well known HARMONIC algorithm,han- dles the general case with competitive ratio ρ<*** sec- ond...
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Two on-line algorithms for variable-size and variable-cost bin packing problems are *** first algo- rithm,based on the well known HARMONIC algorithm,han- dles the general case with competitive ratio ρ<*** sec- ond one focuses on a special case which gives an even smaller ratio.
Previous work on the partial Latin square extension (PLSE) problem resulted in a 2-approximation algorithm based on the LP relaxation of a three-dimensional assignment IP formulation. We present an e/(e - I)-approxima...
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Previous work on the partial Latin square extension (PLSE) problem resulted in a 2-approximation algorithm based on the LP relaxation of a three-dimensional assignment IP formulation. We present an e/(e - I)-approximation algorithm that is based on the LP relaxation of a packing IP formulation of the PLSE problem. (C) 2003 Published by Elsevier B.V.
Given an edge-weighted tree T and an integer p greater than or equal to 1, the minmax p-traveling salesmen problem on a tree T asks to find p tours such that the union of the p tours covers all the vertices. The objec...
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Given an edge-weighted tree T and an integer p greater than or equal to 1, the minmax p-traveling salesmen problem on a tree T asks to find p tours such that the union of the p tours covers all the vertices. The objective is to minimize the maximum of length of the p tours. It is known that the problem is NP-hard and has a (2 - 2/(p+1))-approximation algorithm which runs in O(p(P-1)n(P-1)) time for a tree with n vertices. In this paper, we consider an extension of the problem in which the set of vertices to be covered now can be chosen as a subset S of vertices and weights to process vertices in S are also introduced in the tour length. For the problem, we give an approximation algorithm that has the same performance guarantee, but runs in O((p - 1)! . n) time. (C) 2003 Elsevier B.V. All rights reserved.
Breakpoint graph decomposition is a crucial step in all recent approximation algorithms for SORTING BY REVERSALS, which is one of the best-known algorithmic problems in computational molecular biology. Caprara and Riz...
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Breakpoint graph decomposition is a crucial step in all recent approximation algorithms for SORTING BY REVERSALS, which is one of the best-known algorithmic problems in computational molecular biology. Caprara and Rizzi recently improved the approximation ratio for breakpoint graph decomposition from 3/2 to 33/23 + epsilon approximate to 1.4348 + epsilon, for any positive epsilon. In this paper, we extend the techniques of Caprara and Rizzi and incorporate a balancing argument to further improve the approximation ratio to 5073-15root1201/3208 + epsilon approximate to 1.4193 + epsilon, for any positive epsilon. These improvements imply improved approximation results for SORTING BY REVERSALS for almost all random permutations.
We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, whic...
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We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P not equal NP. (C) 2004 Elsevier B.V. All rights reserved.
In this paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems. Special cases that are covered by our result show...
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In this paper we develop an easily applicable algorithmic technique/tool for developing approximation schemes for certain types of combinatorial optimization problems. Special cases that are covered by our result show up in many places in the literature. For every such special case, a particular rounding trick has been implemented in a slightly different way, with slightly different arguments. and with slightly different worst case estimations. Usually, the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument. Our easily applied result unifies many of these results. and sometimes it even leads to a simpler proof. We demonstrate how our result can be easily applied to a broad family of combinatorial optimization problems. As a special case. we derive the existence of an FPTAS for the scheduling problem of minimizing the weighted number of late jobs under release dates and preemption on a single machine. The approximability status of this problem has been open for some time. (c) 2007 Elsevier B.V. All rights reserved.
In this paper, we study the relationship between the approximability and the parameterized complexity of NP optimization problems. We introduce a notion of polynomial fixed-parameter tractability and prove that, under...
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In this paper, we study the relationship between the approximability and the parameterized complexity of NP optimization problems. We introduce a notion of polynomial fixed-parameter tractability and prove that, under a very general constraint, an NP optimization problem has a fully polynomial time approximation scheme if and only if the problem is polynomial fixed-parameter tractable. By enforcing a constraint of planarity on the W-hierarchy studied in parameterized complexity theory, we obtain a class of NP optimization problems, the planar W-hierarchy, and prove that all problems in this class have efficient polynomial time approximation schemes (EPTAS). The planar W-hierarchy seems to contain most of the known EPTAS problems, and is significantly different from the class introduced by Khanna and Motwani in their efforts in characterizing optimization problems with polynomial time approximation schemes. (c) 2006 Elsevier B.V. All rights reserved.
A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace. The Black Hole Search is the task of locating all black...
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A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace. The Black Hole Search is the task of locating all black holes in a network by exploring it with mobile agents. We consider the problem of designing the fastest Black Hole Search, given the map of the network and the starting node. We study the version of this problem that assumes that there is at most one black hole in the network and there are two agents, which move in synchronized steps. We prove that this problem is NP-hard in arbitrary graphs (even in planar graphs), solving an open problem stated in [J. Czyzowicz, D. Kowalski, E. Markou, A. Pelc, Searching for a black hole in tree networks, in: Proc. 8th Int. Conf. on Principles of Distributed Systems, OPODIS 2004, 2004, pp. 34-35. Also: Springer LNCS, vol. 33/8-approximation algorithm, showing the first non-trivial approximation ratio upper bound for this pp. 67-801, We also give a 3 3 problem. Our algorithm follows a natural approach of exploring networks via spanning trees. We prove that this approach cannot lead to an approximation ratio bound better than 3/2. (C) 2007 Elsevier B.V. All rights reserved.
In this paper,we consider a class of quadratic maximization *** a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the worst-case performance ratio at leastα=0.8...
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In this paper,we consider a class of quadratic maximization *** a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the worst-case performance ratio at leastα=0.87856….In fact,the estimated worst-case performance ratio is dependent on the data of the problem withαbeing a uniform lower *** light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at leastα+δ_d if every weight is strictly positive,whereδ_d>0 is a constant depending on the problem dimension and data.
A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace. The Black Hole Search is the task of locating all black...
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ISBN:
(纸本)3540260528
A black hole is a highly harmful stationary process residing in a node of a network and destroying all mobile agents visiting the node without leaving any trace. The Black Hole Search is the task of locating all black holes in a network by exploring it with mobile agents. We consider the problem of designing the fastest Black Hole Search, given the map of the network and the starting node. We study the version of this problem that assumes that there is at most one black hole in the network and there are two agents, which move in synchronized steps. We prove that this problem is NP-hard in arbitrary graphs (even in planar graphs), solving an open problem stated in [J. Czyzowicz, D. Kowalski, E. Markou, A. Pelc, Searching for a black hole in tree networks, in: Proc. 8th Int. Conf. on Principles of Distributed Systems, OPODIS 2004, 2004, pp. 34-35. Also: Springer LNCS, vol. 33/8-approximation algorithm, showing the first non-trivial approximation ratio upper bound for this pp. 67-801, We also give a 3 3 problem. Our algorithm follows a natural approach of exploring networks via spanning trees. We prove that this approach cannot lead to an approximation ratio bound better than 3/2. (C) 2007 Elsevier B.V. All rights reserved.
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