In this paper, we study a multiple-terminal extension of the classic Hamiltonian path problem where m salesmen are initially located at different depots and finally stopped at different terminals. To the best of our k...
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In this paper, we study a multiple-terminal extension of the classic Hamiltonian path problem where m salesmen are initially located at different depots and finally stopped at different terminals. To the best of our knowledge, only 2-approximation algorithm is available in the literature. For arbitrary m >= 2, we first present a Christofides-like heuristic with a tight approximation ratio of 2-1/2m+1. Besides, we also develop a (5/4 + epsilon)-approximation algorithm by divide-and-conquer technique. The (5/4 + epsilon) -approximation algorithm runs in polynomial time for fixed m and E. (C) 2019 Elsevier B.V. All rights reserved.
Given a connected graph G=(V,E), the Connected Vertex Cover (CVC) problem is to find a vertex set SV with minimum cardinality such that every edge is incident to a vertex in S, and moreover, the induced graph G[S] is ...
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Given a connected graph G=(V,E), the Connected Vertex Cover (CVC) problem is to find a vertex set S< subset of>V with minimum cardinality such that every edge is incident to a vertex in S, and moreover, the induced graph G[S] is connected. In this paper, we investigate the CVC problem in k-regular graphs for any fixed k (k4). First, we prove that the CVC problem is NP-hard for k-regular graphs,and then we give a lower bound for the minimum size of a CVC, based on which, we propose a < approximation algorithm for the CVC problem.
We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due dat...
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We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP-hard even if all the jobs have a unit weight, (ii) the problem is binary NP-hard and admits a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.
The very limited sensor battery energy greatly hinders the large-scale, long-term deployments of wireless sensor networks. This paper studies the problem of scheduling the minimum charging vehicles to charge lifetime-...
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The very limited sensor battery energy greatly hinders the large-scale, long-term deployments of wireless sensor networks. This paper studies the problem of scheduling the minimum charging vehicles to charge lifetime-critical sensors in a wireless rechargeable sensor network, by utilizing the breakthrough wireless charging technology. Existing studies still employ a number of charging vehicles to charge sensors. The purchase cost of a charging vehicle however is not inexpensive. To further reduce the number of employed charging vehicles, we propose a novel approximation algorithm, by exploring the combinatorial properties of the problem. The techniques exploited in this paper are essentially different from that in existing studies. Not only do we show that the approximation ratio of the proposed algorithm is much better than that of the state-of-the-art, but also extensive experimental results demonstrate that the number of scheduled charging vehicles by the proposed algorithm is at least 10% less than that by the existing algorithms and the total travel energy consumption of the charging vehicles is also smaller than that by the existing algorithms.
The multiobjective set covering problem (MOSCP), an NP-hard combinatorial optimization problem, has received limited attention in the literature from the perspective of approximating its Pareto set. The available algo...
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The multiobjective set covering problem (MOSCP), an NP-hard combinatorial optimization problem, has received limited attention in the literature from the perspective of approximating its Pareto set. The available algorithms for approximating the Pareto set do not provide a bound for the approximation error. In this study, a polynomial-time algorithm is proposed to approximate an element in the weak Pareto set of the MOSCP with a quality that is known. A tolerance function is defined to identify the approximation quality and is derived for the proposed algorithm. It is shown that the tolerance function depends on the characteristics of the problem and the weight vector that is used for computing the approximation. For a set of weight vectors, the algorithm approximates a subset of the weak Pareto set of the MOSCP.
Caching at base stations (BSs) can enhance the performance of a mobile network, which has gained much attention in the past few years. In this paper, we investigate the energy-saving issue in the cache-enabled mobile ...
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Caching at base stations (BSs) can enhance the performance of a mobile network, which has gained much attention in the past few years. In this paper, we investigate the energy-saving issue in the cache-enabled mobile network, where we try to minimize the total system power consumption with limited radio resource and storage capacity of the BSs. We decouple the formulated difficult optimization task into a series of tractable subproblems and develop efficient algorithms to solve them with reasonable computation load. The key idea of our proposed scheme is to associate as many as possible users with the BSs that have stored the users' requested files in their caches while considering the spectrum and power budgets of the BSs. Numerical results show our proposed scheme can significantly reduce the system power consumption compared with others.
Datacenter networks are critical to cloud computing. The coflow abstraction is a major leap forward of application-aware network scheduling. In the context of multi-stage jobs, there are dependencies among coflows. As...
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Datacenter networks are critical to cloud computing. The coflow abstraction is a major leap forward of application-aware network scheduling. In the context of multi-stage jobs, there are dependencies among coflows. As a result, there is a large divergence between coflow-completion-time (CCT) and job completion-time (JCT). To our best knowledge, this is the first work that systematically studies: how to schedule dependent coflows of multi-stage jobs, so that the total weighted job completion time can be minimized. We present a formal mathematical formulation. Inspired by the optimal solution of the relaxed linear programming, we design an algorithm that runs in polynomial time to solve this problem with an approximation ratio of (2M + 1) in general case, and 3 in special case, where M is the number of hosts. Evaluation results demonstrate that, the largest gap between our algorithm and the lower bound is only 9.14%. In testbeds, we reduce the JCT by up to 81.65% comparing with pure DCTCP. In simulations, we reduce the average JCT by up to 33.48% comparing with Aalo, a heuristic multi-stage coflow scheduler;we reduce the total weighted JCT by up to 83.58% comparing with LP-OV-LS, the state-of-the-art approximation algorithm of coflow scheduling. (C) 2019 Elsevier B.V. All rights reserved.
In this article, we study an approximation algorithm for the maximum edge-disjoint paths problem. In this problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum n...
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In this article, we study an approximation algorithm for the maximum edge-disjoint paths problem. In this problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be connected by edge-disjoint paths. We give an O(log n)-approximation algorithm for the maximum edge-disjoint paths problem when an input graph is either 4-edge-connected planar or Eulerian planar. This improves an O(log(2) n)-approximation algorithm given by Kleinberg [2005] for Eulerian planar graphs. Our result also generalizes the result by Chekuri et al. [2004, 2005] who gave an O(log n)-approximation algorithm for the maximum edge-disjoint paths problem with congestion two when an input graph is planar.
The widespread and effective online social networks may cause misinformation to diffuse in the networks, which could lead to public panic and even serious economic consequences. The classical misinformation containmen...
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The widespread and effective online social networks may cause misinformation to diffuse in the networks, which could lead to public panic and even serious economic consequences. The classical misinformation containment (MC) problem aims to select a small node set as positive seeds to compete against the misinformation and limit the influence of misinformation as much as possible, where the misinformation seed set is given. Most of the prior works concentrate on either minimizing the number of users infected by misinformation or maximizing the number of users protected by the positive cascade. That is, they only concentrate on optimizing the number of nodes. However, the interaction effects between nodes differ from user to user and the related profit obtained from interaction activities may also be different. This article proposes a novel problem, called profit minimization of misinformation (PMM), which is the first to analyze the profit of activity in the MC problem. Given a misinformation seed set, the PMM problem aims at selecting a node set satisfying the cardinality constraint to minimize the profit of edges starting from infected nodes but ending at infected or protected nodes. Based on the sandwich method, we design a data-dependent approximation scheme for the PMM problem. We approximate the upper and lower bounds of the objective in the equivalent problem by the reverse influence sampling technique. Our algorithm is verified on realistic data sets, which demonstrate the superiority of our method.
This paper addresses the problem of scheduling on batch and unary machines with incompatible job families such that the total weighted completion time is minimised. A mixed-integer linear programming model is proposed...
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This paper addresses the problem of scheduling on batch and unary machines with incompatible job families such that the total weighted completion time is minimised. A mixed-integer linear programming model is proposed to solve the problem to optimality for small instances. Tight lower bounds and a 4-approximation algorithm are developed. A constraint programming-based method is also proposed. Numerical results demonstrate that the proposed algorithms can obtain high quality solutions and have a competitive performance. Sensitivity analysis indicates that the performance of the proposed algorithms is also robust on different problem structures.
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