We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r(j) facilities instead of ju...
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We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r(j) facilities instead of just one. The facilities other than the closest one are "backup" facilities for that demand, and any such facility will be used only if all closer facilities (or the links to them) fail. Hence, for any demand point, we can assign nonincreasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r(j) closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve the approximation ratio to 3.16 using randomization and to 2.41 using greedy local-search type techniques. (C) 2003 Elsevier Inc. All rights reserved.
The uncapacitated facility location problem in the following formulation is considered: max(S subset of or equal to I) Z(S) = Sigma(j is an element of J)max(i is an element of S)b(ij) - Sigma(i is an element of S)c(i)...
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The uncapacitated facility location problem in the following formulation is considered: max(S subset of or equal to I) Z(S) = Sigma(j is an element of J)max(i is an element of S)b(ij) - Sigma(i is an element of S)c(i), where I and J are finite sets, and b(ij), c(i)greater than or equal to 0 are rational numbers. Let Z* denote the optimal value of the problem and let Z(R) = Sigma(j is an element of J)min(i is an element of I)b(ij) - Sigma(i is an element of I)c(i). Cornuejols et al. (Ann. Discrete Math. 1 (1977) 163-178) prove that for the problem with the additional cardinality constraint \S\less than or equal to K, a simple greedy algorithm finds a feasible solution S such that (Z(S) - ZR)/(Z* - ZR)greater than or equal to 1 - e(-1) approximate to 0.632. We suggest a polynomial-time approximation algorithm for the unconstrained version of the problem, based on the idea of randomized rounding due to Goemans and Williamson (SIAM J. Discrete Math. 7 (1994) 656 - 666). It is proved that the algorithm delivers a solution S such that (Z(S) - Z(R))/(Z* - Z(R))greater than or equal to 2(root 2 - 1) approximate to 0.828. We also show that there exists epsilon > 0 such that it is NP-hard to find an approximate solution S with (Z(S) - Z(R))/(Z* - Z(R))greater than or equal to 1 - epsilon. (C) 1999 Elsevier Science B.V. All rights reserved.
The translocation operation is one of the popular operations for genome rearrangement. In this paper, we present a algorithm for computing unsigned translocation distance which improves upon the best known 2-approxima...
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The translocation operation is one of the popular operations for genome rearrangement. In this paper, we present a algorithm for computing unsigned translocation distance which improves upon the best known 2-approximation algorithm [J. Kececioglu, R. Ravi, Of mice and men: algorithms for evolutionary distances between genomes with translocation, in: 6th ACM-SIAM Symposium on Discrete algorithms, 1995, pp. 604-6131. (c) 2007 Elsevier Inc. All rights reserved.
We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete algorithms (SODA), pp. 933-942, 2005), ...
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We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete algorithms (SODA), pp. 933-942, 2005), who presented a 2.50-approximation algorithm that is non-combinatorial because this algorithm has to solve the LP-relaxation of an integer program with exponential number of variables. The only known polynomial algorithm for this exponential LP is via the ellipsoid algorithm as the corresponding separation problem for its dual program can be solved in polynomial time. By exploring the properties of the submodular function, we offer a primal-dual 3-approximation combinatorial algorithm for this problem.
An l-pseudoforest is a graph each of whose connected components is at most I edges removal being a tree. The l-Pseudoforest Deletion problem is to delete a vertex set P of minimum weight from a given vertex-weighted g...
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An l-pseudoforest is a graph each of whose connected components is at most I edges removal being a tree. The l-Pseudoforest Deletion problem is to delete a vertex set P of minimum weight from a given vertex-weighted graph G = (V, E) such that the remaining graph G[V \ P] is an l-pseudoforest The Feedback Vertex Set problem is a special case of the l-Pseudoforest Deletion problem with l = 0. In this paper, we present a polynomial time 41-approximation algorithm for the l-Pseudoforest Deletion problem with l >= 1 by using the local ratio technique. When l=1, we get a better approximation ratio 2 for the problem by further analyzing the local ratio, which matches the current best constant approximation factor for the Feedback Vertex Set problem. (C) 2019 Elsevier B.V. All rights reserved.
We consider the following planar maximum weight triangulation (MAT) problem: given a set of n points in the plane, find a triangulation such that the total length of edges in triangulation is maximized. We prove an Om...
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We consider the following planar maximum weight triangulation (MAT) problem: given a set of n points in the plane, find a triangulation such that the total length of edges in triangulation is maximized. We prove an Omega(root n) lower bound on the approximation factor for several heuristics: maximum greedy triangulation, maximum greedy spanning tree triangulation and maximum spanning tree triangulation. We then propose the Spoke Triangulation algorithm, which approximates the maximum weight triangulation for points in general position within a factor of almost four in O(n log n) time. The proof is simpler than the previous work. We also prove that Spoke Triangulation approximates the maximum weight triangulation of a convex polygon within a factor of two.
This paper studies approximation algorithm for the maximum weight budgeted connected set cover (MWBCSC) problem. Given an element set , a collection of sets , a weight function on , a cost function on , a connected gr...
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This paper studies approximation algorithm for the maximum weight budgeted connected set cover (MWBCSC) problem. Given an element set , a collection of sets , a weight function on , a cost function on , a connected graph (called communication graph) on vertex set , and a budget , the MWBCSC problem is to select a subcollection such that the cost , the subgraph of induced by is connected, and the total weight of elements covered by (that is ) is maximized. We present a polynomial time algorithm for this problem with a natural communication graph that has performance ratio , where is the maximum degree of graph and is the number of sets in . In particular, if every set has cost at most , the performance ratio can be improved to .
There is an error in our paper "An approximation algorithm fur Minimum-Cost Vertex-Connectivity Problems" (algorithmica (1997), 18:21-43). In that paper we considered the following problem: given an undirect...
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There is an error in our paper "An approximation algorithm fur Minimum-Cost Vertex-Connectivity Problems" (algorithmica (1997), 18:21-43). In that paper we considered the following problem: given an undirected graph and values r(ij) for each pair of vertices i and j, find a minimum-cost set of edged, such that there are r(ij) vertex-disjoint paths between vertices i and j. We gave approximation algorithms for two special cases of this problem. Our algorithms rely on a primal-dual approach which has led to approximation El algorithms for many edge-connectivity problems, The algorithms work in a series of stages;in each stage an augmentation subroutine augments the connectivity of the current solution. The error is in a lemma for the proof of the performance guarantee of the augmentation subroutine. In the case r(ij) = k for all i, j, we described a polynomial-time algorithm that claimed to output a solution of cost no more than 27-l(k) times optimal, where H(n) 1 + 1/2 + ... + 1/n. This result is erroneous. We describe an example where our primal-dual augmentation subroutine, when augmenting a k-vertex connected graph to a (k + 1)-vertex connected graph, gives solutions that are a factor n (k) away from the minimum, In the case r(ij) is an element of {0, 1, 2} for all i, j, we gave a polynomial-time algorithm which outputs a solution of cost no more than three times the optimal. In this case we prove that the statement in the lemma that was erroneous for the k-vertex connected case does hold, and that the algorithm performs as claimed.
Smart grid is in need of an efficient communication network to guarantee reliable two-way data transmission between the control center and smart meters (SMs). In this work, a software-defined networking (SDN) based sm...
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Smart grid is in need of an efficient communication network to guarantee reliable two-way data transmission between the control center and smart meters (SMs). In this work, a software-defined networking (SDN) based smart grid communication (SGC) scheme is introduced to fulfill the information transmission requirement, where the control plane is separated from the data plane to support diverse services flexibly in the smart grid. In such an SDN-based SGC system, to guarantee effective data processing and forwarding between the SMs and the control center, aggregation points (APs) are introduced. These APs should be deployed in an optimal way so as to cut down the total capital expenditure of the SGC system. The total cost generally includes the transmission cost between APs and the control center as well as APs and SMs. The construction and maintenance cost of the APs is also included. An approximation algorithm is introduced in this paper. The algorithm can deal with the formulated intractable APs planning task and produce performance-guaranteed solutions with reasonable complexity. Experiments indicate that the proposed algorithm works well for geographical areas with different densities of SMs. Our proposal yields cost-efficient APs deployment scheme and sheds insight into the reduction of the capital expenditure of the SGC system.
The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimen...
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The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a ([D-s/2] + 1)/([log(2)(D-s + 1)] + 1)-approximation algorithm for MVRST where D-s is the minimum diameter of spanning trees of G. (c) 2006 Elsevier B.V. All rights reserved.
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