In wireless sensor networks, a virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem and perform some other tasks such as area monitoring. Previous work in this a...
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In wireless sensor networks, a virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem and perform some other tasks such as area monitoring. Previous work in this area has mainly focused on how to set up a small virtual backbone for high efficiency, which is modelled as the minimum Connected Dominating Set (CDS) problem. In this paper we consider how to establish a small virtual backbone to balance efficiency and fault tolerance. This problem can be formalized as the minimum m-connected k-tuple dominating set problem, which is a general version of minimum CDS problem with m = 1 and k = 1. We propose three centralized algorithms with small approximation ratios for small m and improve the current best results for small k. (c) 2007 Elsevier B.V. All rights reserved.
We consider a generalization of the classical MAX-CUT problem where two objective functions are simultaneously considered. We derive some theorems on the existence and the non-existence of feasible cuts that are at th...
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We consider a generalization of the classical MAX-CUT problem where two objective functions are simultaneously considered. We derive some theorems on the existence and the non-existence of feasible cuts that are at the same time near optimal for both criteria. Furthermore, two approximation algorithms with performance guarantee are presented. The first one is deterministic while the second one is randomized. A generalization of these results is given for the bi-criteria MAX-k-CUT problem. (c) 2006 Elsevier B.V. All rights reserved.
Consider a network of k servers and their users. Each server provides a unique service that has a certain utility for each user. Now comes an attacker who wishes to destroy a set of network edges to maximize his net g...
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Consider a network of k servers and their users. Each server provides a unique service that has a certain utility for each user. Now comes an attacker who wishes to destroy a set of network edges to maximize his net gain, namely the total disconnected utilities of the users minus the total edge-destruction cost. This k-server disconnection problem is NP-hard and, furthermore, cannot be approximated within a polynomially computable factor of the optimum when k is part of the input. Even for any fixed k >= 2, there is a constant epsilon > 0 such that approximation of the problem within a factor 1/(1 + epsilon) of the optimum is NP-hard. However, a (1/2 + 1/2(k+1)-2)-approximation can be created in the time of 0(2 k) applications of a min-cut algorithm. The main idea is to approximate the optimum with special solutions computable in polynomial time due to supermodularity. Therefore, when the the network has, as is usual in most cases, only a few servers, a 0.5-approximation can be carried out in polynomial time. (c) 2007 Wiley Periodicals, Inc.
We consider a single-machine scheduling problem with periodic maintenance activities. Although the scheduling problem with maintenance has attracted researchers' attention, most of past studies considered only one...
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We consider a single-machine scheduling problem with periodic maintenance activities. Although the scheduling problem with maintenance has attracted researchers' attention, most of past studies considered only one maintenance period. In this research several maintenance periods are considered where each maintenance activity is scheduled after a periodic time interval. The objective is to find a schedule that minimizes the makespan, subject to periodic maintenance and nonresumable jobs. We first prove that the worst-case ratio of the classical LPT algorithm is 2. Then we show that there is no polynomial time approximation algorithm with a worst-case ratio less than 2 unless P = NP, which implies that the LPT algorithm is the best possible. (c) 2005 Elsevier Ltd. All rights reserved.
Given an undirected graph with nonnegative weights on its edges, a group of source nodes, and a group of destination nodes, we investigate the problem of constructing a multicast tree that minimizes the sum of distanc...
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Given an undirected graph with nonnegative weights on its edges, a group of source nodes, and a group of destination nodes, we investigate the problem of constructing a multicast tree that minimizes the sum of distances from a destination node to all sources. This problem has been proven to be NP-complete. In this article, we show that there is a point c of the graph such that a shortest paths tree constructed from c is a 2-approximation to the problem, a significant improvement over the previous results, and we present an efficient approximation algorithm. (c) 2006 Wiley Periodicals, Inc.
We analyze a list heuristic for the vertex cover problem that handles the vertices in a given static order based on the degree sequence. We prove an approximation ratio of at most root Delta/2+(3/)(2) for a nonincreas...
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We analyze a list heuristic for the vertex cover problem that handles the vertices in a given static order based on the degree sequence. We prove an approximation ratio of at most root Delta/2+(3/)(2) for a nonincreasing degree sequence, and show that no ordering can achieve an approximation ratio of less than root Delta/2. (c) 2006 Elsevier B.V. All rights reserved.
In the order scheduling problem, every job (order) consists of several tasks (product items), each of which will be processed on a dedicated machine. The completion time of a job is defined as the time at which all it...
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In the order scheduling problem, every job (order) consists of several tasks (product items), each of which will be processed on a dedicated machine. The completion time of a job is defined as the time at which all its tasks are finished. Minimizing the number of late jobs was known to be strongly NP-hard. In this note, we show that no FPTAS exists for the two-machine, common due date case, unless P = NP. We design a heuristic algorithm and analyze its performance ratio for the unweighted case. An LP-based approximation algorithm is presented for the general multicover problem. The algorithm can be applied to the weighted version of the order scheduling problem with a common due date. (c) 2006 Elsevier B.V. All rights reserved.
For a bounded integer l, we wish to color all edges of a graph G so that any two edges within distance l have different colors. Such a coloring is called a distance-edge-coloring or an l-edge-coloring of G. The distan...
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For a bounded integer l, we wish to color all edges of a graph G so that any two edges within distance l have different colors. Such a coloring is called a distance-edge-coloring or an l-edge-coloring of G. The distance-edge-coloring problem is to compute the minimum number of colors required for a distance-edge-coloring of a given graph G. A partial k-tree is a graph with tree-width bounded by a fixed constant k. We first present a polynomial-time exact algorithm to solve the problem for partial k-trees, and then give a polynomial-time 2-approximation algorithm for planar graphs. (C) 2006 Elsevier B.V. All rights reserved.
Using flow and matching algorithms to solve the problem of finding disjoint paths through a given node, and with a technique of Chekuri and Khanna, we give an 0(root n) approximation for the edge-disjoint paths proble...
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Using flow and matching algorithms to solve the problem of finding disjoint paths through a given node, and with a technique of Chekuri and Khanna, we give an 0(root n) approximation for the edge-disjoint paths problem in undirected graphs, directed acyclic graphs and directed graphs with edge capacity at least 2. (c) 2006 Elsevier B.V. All rights reserved.
Given a hypergraph and k different colors, we study the problem of packing and coloring a subset of the hyperedges of the hypergraph as paths in a cycle such that the total profit of the hyperedges selected is maximiz...
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Given a hypergraph and k different colors, we study the problem of packing and coloring a subset of the hyperedges of the hypergraph as paths in a cycle such that the total profit of the hyperedges selected is maximized, where each physical link e(j) on the cycle is used at most c(j) times, each hyperedge hi has its profit pi and any two paths, each spanning all nodes of its corresponding hyperedge, must be assigned different colors if they share a common physical link. This new problem arises in optical communication networks, and it is called the Maximizing Profits when Packing and Coloring Hyperedges in a Cycle problem (MPPCHC). In this paper, we prove that the MPPCHC problem is NP-hard and then present an algorithm with approximation ratio 2 for this problem. For the special case where each hyperedge has the same profit I and each link ej has same capacity k, we propose an algorithm with approximation ratio 3/2 (C) 2007 Elsevier B.V. All rights reserved.
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