We consider the vertex cover P-n (VCPn) problem, that is, the problem of finding a minimum weight set F subset of V such that the graph G[V - F] has no P-n, where P-n is a path with n vertices. The problem also has it...
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We consider the vertex cover P-n (VCPn) problem, that is, the problem of finding a minimum weight set F subset of V such that the graph G[V - F] has no P-n, where P-n is a path with n vertices. The problem also has its application background. In this paper, we restrict our attention to the VCP3 problem and give a 2-approximation algorithm using the technique of layering. (C) 2011 Elsevier B.V. All rights reserved.
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.
In this letter, we study the optimum selection of ground stations (GSs) in RF/optical satellite networks (SatNets) in order to minimize the overall installation cost under an outage probability requirement, assuming i...
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In this letter, we study the optimum selection of ground stations (GSs) in RF/optical satellite networks (SatNets) in order to minimize the overall installation cost under an outage probability requirement, assuming independent weather conditions between sites. First, we show that the optimization problem can be formulated as a binary-linear-programming problem, and then we give a formal proof of its NP-hardness. Furthermore, we design a dynamic-programming algorithm of pseudo-polynomial complexity with global optimization guarantee as well as an efficient (polynomial-time) approximation algorithm with provable performance guarantee on the distance of the achieved objective value from the global optimum. Finally, the performance of the proposed algorithms is verified through numerical simulations.
A partitionable multiprocessor system can form multiple partitions, each consisting of a controller and a varying number of processors. Given such a system and a set of tasks, each of which can be executed on partitio...
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A partitionable multiprocessor system can form multiple partitions, each consisting of a controller and a varying number of processors. Given such a system and a set of tasks, each of which can be executed on partitions of varying sizes, we study the problem of choosing the partition sizes and a minimum completion time schedule for the execution of these tasks. We assume that the number of tasks to be scheduled on the system is no more than the maximum number of partitions that can be formed simultaneously by the system, and that parallelization of the tasks can achieve at most perfect speedup. We show this scheduling problem to be NP-hard, and present a polynomial time approximation algorithm for this problem. We derive a parameter dependent, asymptotically tight worst-case performance bound for this approximation algorithm. We also evaluate its average performance through simulation.
The jump number of a partial order P is the minimum number of incomparable adjacent pairs in some linear extension of P. The jump number problem is known to be NP-hard in general. However some particular classes of po...
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The jump number of a partial order P is the minimum number of incomparable adjacent pairs in some linear extension of P. The jump number problem is known to be NP-hard in general. However some particular classes of posets admit easy calculation of the jump number.
The complexity status for interval orders still remains unknown. Here we present a heuristic that, given an interval order P, generates a linear extension Λ, whose jump number is less than 3/2 times the jump number of P.
Mehlhorn (1988) has presented an improved implementation of the Kou, Markowsky and Berman Steiner tree approximation algorithm (1981). By replacing one step of the original algorithm the complexity reduces from O(\S\....
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Mehlhorn (1988) has presented an improved implementation of the Kou, Markowsky and Berman Steiner tree approximation algorithm (1981). By replacing one step of the original algorithm the complexity reduces from O(\S\.(\E\ + \V\.log\V\) to O(\E\ + \V\.log\V\), where S is the set of terminals, E the set of all edges and V the set of all vertices in the graph. In this paper we will show that due to the improvement two steps of the algorithm may be omitted. This does not reduce the complexity of the algorithm but it makes it simpler.
We consider the problem of partitioning a finite sequence of points in Euclidean space into a given number of clusters (subsequences) minimizing the sum over all clusters of intracluster sums of squared distances of e...
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We consider the problem of partitioning a finite sequence of points in Euclidean space into a given number of clusters (subsequences) minimizing the sum over all clusters of intracluster sums of squared distances of elements of the clusters to their centers. It is assumed that the center of one of the desired clusters is the origin, while the centers of the other clusters are unknown and are defined as the mean values of cluster elements. Additionally, there are a few structural constraints on the elements of the sequence that enter the clusters with unknown centers: (1) the concatenation of indices of elements of these clusters is an increasing sequence, (2) the difference between two consequent indices is lower and upper bounded by prescribed constants, and (3) the total number of elements in these clusters is given as an input. It is shown that the problem is strongly NP-hard. A 2-approximation algorithm that is polynomial for a fixed number of clusters is proposed for this problem.
We consider the scheduling problem in which jobs with release times and delivery times are to be scheduled on one machine. We present a 3/2-approximation algorithm which runs in O(n log n) time and a new robust lower ...
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We consider the scheduling problem in which jobs with release times and delivery times are to be scheduled on one machine. We present a 3/2-approximation algorithm which runs in O(n log n) time and a new robust lower bound for this problem. The known until the present 3/2-approximation algorithm has O(n (2)log n) computational complexity.
Genome rearrangement algorithms are powerful tools to analyze gene orders in molecular evolution. Analysis of genomes evolving by reversals and transpositions leads to a combinatorial problem of sorting by reversals a...
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Genome rearrangement algorithms are powerful tools to analyze gene orders in molecular evolution. Analysis of genomes evolving by reversals and transpositions leads to a combinatorial problem of sorting by reversals and transpositions, the problem of finding a shortest sequence of reversals and transpositions that sorts one genome into the other. In this paper we present a 2k-approximation algorithm for sorting by reversals and transpositions for unsigned permutations where k is the approximation ratio of the algorithm used for cycle decomposition. For the best known value of k our approximation ratio becomes 2.8386 + delta for any delta > 0. We also derive a lower bound on reversal and transposition distance of an unsigned permutation. (C) 2007 Elsevier B.V. All rights reserved.
Given a directed graph G and an arc weight function w : E(G) --> R+, the maximum directed cut problem (MAX DICUT) is that of finding a directed cut delta (X) with maximum total weight. In this paper we consider a v...
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Given a directed graph G and an arc weight function w : E(G) --> R+, the maximum directed cut problem (MAX DICUT) is that of finding a directed cut delta (X) with maximum total weight. In this paper we consider a version of MAX DICUT-MAX DICUT with given sizes of parts or MAX DICUT WITH GSP-whose instance is that of MAX DICUT plus a positive integer p, and it is required to nd a directed cut delta (X) having maximum weight over all cuts delta (X) with |X| = p. Our main result is a 0.5-approximation algorithm for solving the problem. The algorithm is based on a tricky application of the pipage rounding technique developed in some earlier papers by two of the authors and a remarkable structural property of basic solutions to a linear relaxation. The property is that each component of any basic solution is an element of a set {0,delta ,1/2,1-delta ,1}, where delta is a constant that satisfies 0 < < 1/2 and is the same for all components.
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