The traditional approach for the problems of sorting permutations by rearrangements is to consider that all operations have the same unitary cost. In this case, the goal is to find the minimum number of allowed rearra...
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The traditional approach for the problems of sorting permutations by rearrangements is to consider that all operations have the same unitary cost. In this case, the goal is to find the minimum number of allowed rearrangements that are needed to sort a given permutation, and numerous efforts have been made over the past years regarding these problems. On the other hand, a long rearrangement (which is in fact a mutation) is more likely to disturb the organism. Therefore, weights based on the length of the segment involved may have an important role in the evolutionary process. In this paper we present the first results regarding problems of sorting permutations by length-weighted operations that consider rearrangement models with prefix and suffix variations of reversals and transpositions, which are the two most common types of genome rearrangements. Our main results are O (lg(2) n)-approximation algorithms for 10 such problems. (C) 2015 Elsevier B.V. All rights reserved.
Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed t...
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Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion of pathwidth to digraphs. Directed treewidth, DAG-width and Kelly-width are some such notions which generalize treewidth, whereas directed pathwidth generalizes pathwidth. Each of these digraph width measures have an associated decomposition structure. In this paper, we present approximation algorithms for all these digraph width parameters. In particular, we give an 0 root logn)-approximation algorithm for directed treewidth, and an O (log(3/2) n)-approximation algorithm for directed pathwidth, DAG-width and Kelly-width. Our algorithms construct the corresponding decompositions whose widths agree with the above mentioned approximation factors. (C) 2014 Elsevier B.V. All rights reserved.
In this paper we consider the maximization of the weighted number of early jobs on a single machine with non-availability constraints. We deal with the resumable and the non-resumable cases. We show that the resumable...
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In this paper we consider the maximization of the weighted number of early jobs on a single machine with non-availability constraints. We deal with the resumable and the non-resumable cases. We show that the resumable version of this problem has a fully polynomial time approximation scheme (FPTAS) even if the number of the non-availability intervals is variable and a subset of jobs has deadlines instead of due dates. For the non-resumable version we remark that the problem cannot admit an FPTAS even if all due dates are equal and only one non-availability interval occurs. Nevertheless, we show in this case that it admits a polynomial time approximation scheme (PTAS) for a constant number of non-availability intervals and arbitrary due dates.
Given a graph G = (V. E) a clique is a maximal subset of pairwise adjacent vertices of V of size at least 2. A clique transversal is a subset of vertices that intersects the vertex set of each clique of G. Finding a m...
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Given a graph G = (V. E) a clique is a maximal subset of pairwise adjacent vertices of V of size at least 2. A clique transversal is a subset of vertices that intersects the vertex set of each clique of G. Finding a minimum-cardinality clique transversal is NP-hard for the following classes: planar, line and bounded degree graphs. For line graphs we present a 3-approximation for the unweighted case and a 4-approximation for the weighted case with nonnegative weights;a inverted right perpendicular(G) + 1)/2inverted left perpendicular-approximation for bounded degree graphs and a 3-approximation for planar graphs. (C) 2015 Elsevier B.V. All rights reserved.
We study a revenue maximization problem in the context of social networks. Namely, we consider a model introduced by Alon, Mansour, and Tennenholtz (EC 2013) that captures inequity aversion, i.e., prices offered to ne...
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We study the capacitated k-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a positive integer k. It costs f(i) to open facility i, and c(ij) for ...
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We study the capacitated k-facility location problem, in which we are given a set of clients with demands, a set of facilities with capacities and a positive integer k. It costs f(i) to open facility i, and c(ij) for facility i to serve one unit of demand from client j. The objective is to open at most k facilities serving all the demands and satisfying the capacity constraints while minimizing the sum of service and opening costs. In this paper, we give the first fully polynomial time approximation scheme (FPTAS) for the single-sink (single-client) capacitated k-facility location problem. Then, we show that the capacitated k-facility location problem with uniform capacities is solvable in polynomial time if the number of clients is fixed by reducing it to a collection of transportation problems. Third, we analyze the structure of extreme point solutions, and examine the efficiency of this structure in designing approximation algorithms for capacitated k-facility location problems. Finally, we extend our results to obtain an improved approximation algorithm for the capacitated facility location problem with uniform opening costs. (C) 2014 Elsevier B.V. All rights reserved.
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriou...
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In this article we present approximation algorithms for the Arc Orienteering Problem (AOP). We propose a polylogarithmic approximation algorithm in directed graphs, while in undirected graphs we give a (6 + epsilon + ...
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In this article we present approximation algorithms for the Arc Orienteering Problem (AOP). We propose a polylogarithmic approximation algorithm in directed graphs, while in undirected graphs we give a (6 + epsilon + o(1)) and a (4 + epsilon)-approximation algorithm for arbitrary instances and instances of unit profit, respectively. Also, an inapproximability result for the AOP is obtained as well as approximation algorithms for the Mixed Orienteering Problem. (C) 2014 Elsevier B.V. All rights reserved.
We consider the matroid median problem [Krishnaswamy et al. 2011], wherein we are given a set of facilities with opening costs and a matroid on the facility-set, and clients with demands and connection costs, and we s...
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We consider the matroid median problem [Krishnaswamy et al. 2011], wherein we are given a set of facilities with opening costs and a matroid on the facility-set, and clients with demands and connection costs, and we seek to open an independent set of facilities and assign clients to open facilities so as to minimize the sum of the facility-opening and client-connection costs. We give a simple 8-approximation algorithm for this problem based on LP-rounding, which improves upon the 16-approximation in Krishnaswamy et al. [2011]. We illustrate the power and versatility of our techniques by deriving (a) an 8-approximation for the two-matroid median problem, a generalization of matroid median that we introduce involving two matroids;and (b) a 24-approximation algorithm for matroid median with penalties, which is a vast improvement over the 360-approximation obtained in Krishnaswamy et al. [2011]. We show that a variety of seemingly disparate facility-location problems considered in the literature-data placement problem, mobile facility location, k-median forest, metric uniform minimum-latency Uncapacitated Facility Location (UFL)-in fact reduce to the matroid median or two-matroid median problems, and thus obtain improved approximation guarantees for all these problems. Our techniques also yield an improvement for the knapsack median problem.
Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning sub graphs (or d-factor...
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ISBN:
(纸本)9783319286846;9783319286839
Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning sub graphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d >= 2 . [k/2]. For the case of k-vertex-connectedness, we achieve constant approximation ratios for d >= 2k 1. Our algorithms also work for arbitrary degree sequences if the minimum degree is at least 2 . [k/2] (for k-edge connectivity) or 2k - 1 (for k-vertex-connectivity).
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