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27
A 2approximation algorithm for the undirected feedback vertex set problem
 SIAM J. Discrete Math
, 1999
"... Abstract. A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. The problem considered is that of finding a minimum feedback vertex set given a weighted and undirected graph. We present a simple and efficient approximation algorithm ..."
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Cited by 92 (0 self)
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Abstract. A feedback vertex set of a graph is a subset of vertices that contains at least one vertex from every cycle in the graph. The problem considered is that of finding a minimum feedback vertex set given a weighted and undirected graph. We present a simple and efficient approximation algorithm with performance ratio of at most 2, improving previous best bounds for either weighted or unweighted cases of the problem. Any further improvement on this bound, matching the best constant factor known for the vertex cover problem, is deemed challenging. The approximation principle, underlying the algorithm, is based on a generalized form of the classical local ratio theorem, originally developed for approximation of the vertex cover problem, and a more flexible style of its application.
On Approximation Properties of the Independent Set Problem for Degree 3 Graphs
 In Proc. of Workshop on Algorithms and Data Structures
, 1995
"... . The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SNPcomplete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNPcomplete at the lowest possible degree bounds. N ..."
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Cited by 49 (0 self)
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. The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SNPcomplete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNPcomplete at the lowest possible degree bounds. Next we study better polytime approximation of the problem for degree 3 graphs, and improve the previously best ratio, 5 4 , to arbitrarily close to 6 5 . This result also provides improved polytime approximation ratios, B+3 5 + ffl, for odd degree B. 1 Introduction The area of efficient approximation algorithms for NPhard optimization problems has recently seen dramatic progress with a sequence of breakthrough achievements. Even when restricted only to the area of constant bound approximation the following remarkable results have been obtained in the last few years. The subclass of NP optimization problems, called MAX SNP, consisting solely of constant ratio approximable problems ...
Constant Ratio Approximations of the Weighted Feedback . . .
"... We consider the weighted feedback vertex set problem for undirected graphs. It is shown that a generalized local ratio strategy leads to an efficient approximation with the performance guarantee of twice the optimal, improving the previous results for both weighted and unweighted cases. We further e ..."
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Cited by 23 (4 self)
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We consider the weighted feedback vertex set problem for undirected graphs. It is shown that a generalized local ratio strategy leads to an efficient approximation with the performance guarantee of twice the optimal, improving the previous results for both weighted and unweighted cases. We further elaborate our approach to treat the case when graphs are of bounded degree, and show that it achieves even better performance, 2 0 2 3102 , where 1 is the maximum degree of graphs.
Approximation algorithms for the weighted independent set problem
 IN GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE, 31ST INTERNATIONAL WORKSHOP, WG
, 2005
"... In unweighted case, approximation ratio for the independent set problem has been analyzed in terms of the graph parameters, such as the number of vertices, maximum degree, and average degree. In weighted case, no corresponding results are given for average degree. It is not appropriate that we anal ..."
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Cited by 18 (1 self)
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In unweighted case, approximation ratio for the independent set problem has been analyzed in terms of the graph parameters, such as the number of vertices, maximum degree, and average degree. In weighted case, no corresponding results are given for average degree. It is not appropriate that we analyze weighted independent set algorithms in terms of average degree, since inserting the vertices with small weight decreases average degree arbitrarily without significantly changing approximation ratio. In this paper, we introduce the “weighted ” average degree and “weighted ” inductiveness, and analyze algorithms for the weighted independent set problem in terms of these parameters.
Approximation Algorithms for Submodular Set Cover with Applications
 IEICE Trans. Inf. Syst
, 2000
"... Introduction We start with the set cover( SC ) problem. Given a finite set M and a family N of subsets of M , a subfamily S of N is called a set cover if every element of M appears in some subset in S; in other words, the union of all subsets in S coincides with M . Each set in N is associated w ..."
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Cited by 19 (0 self)
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Introduction We start with the set cover( SC ) problem. Given a finite set M and a family N of subsets of M , a subfamily S of N is called a set cover if every element of M appears in some subset in S; in other words, the union of all subsets in S coincides with M . Each set in N is associated with a (U"C2T0"'# e) cost, and the cost of a family is the sum of costs of subsets in it. The set cover problem then asks to find a minimum cost set cover. As a special case when all the costs associated with sets are identical, it is called the unit cost set cover, and it is one of the basic NPcomplete optimization problems presented by Karp [17]. he problem is also equivalent to the hitting set problem and the dominating set problem on gra
A Simple Approach to Chiral Trifluoromethyl Compounds ………………………6 Club Activities Toyohashi Tech Kyudo Club: Fun through serious practice ………………………7 Excursions Cherry Blossom Viewing Party and Pottery …………………………………………7 Study Tour in Kyoto ……………………………………………
, 2013
"... Growing plants in factories Project Professor Masahiko Saigusa and his team of researchers at Toyohashi Tech’s Research Center for Agrotechnology and Biotechnology are investigating ways of growing vegetables more efficiently using intelligent greenhouses and plant factories. ..."
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Growing plants in factories Project Professor Masahiko Saigusa and his team of researchers at Toyohashi Tech’s Research Center for Agrotechnology and Biotechnology are investigating ways of growing vegetables more efficiently using intelligent greenhouses and plant factories.
A 2 1/10Approximation Algorithm for a Generalization of the Weighted EdgeDominating Set Problem
 In procof &quot;ESA '00
, 2000
"... We study the approximability of the weighted edgedominating set problem. Although even the unweighted case is NPComplete, in this case a solution of size at most twice the minimum can be efficiently computed due to its close relationship with minimum maximal matching; however, in the weighted case ..."
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Cited by 12 (6 self)
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We study the approximability of the weighted edgedominating set problem. Although even the unweighted case is NPComplete, in this case a solution of size at most twice the minimum can be efficiently computed due to its close relationship with minimum maximal matching; however, in the weighted case such a nice relationship is not known to exist. In this paper, after showing that weighted edge domination is as hard to approximate as the well studied weighted vertex cover problem, we consider a natural strategy, reducing edgedominating set to edge cover. Our main result is a simple 2 1/10approximation algorithm for the weighted edgedominating set problem, improving the existing ratio, due to a simple reduction to weighted vertex cover, of 2rWVC , where rWVC is the approximation guarantee of any polynomialtime weighted vertex cover algorithm. The best value of rWVC currently stands at 2 log log V 2 log V. Furthermore we establish that the factor of 2 1/10 is...
Approximating Minimum Spanning Sets in Hypergraphs and Polymatroids
, 2000
"... We present a new analysis of the greedy algorithm for the problem of finding a minimum spanning subset in kpolymatroids. This algorithm has a performance ratio of approximately ln k, which is best possible for large k. A consequence of this algorithm is a polynomial time approximation algorithm ..."
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Cited by 4 (2 self)
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We present a new analysis of the greedy algorithm for the problem of finding a minimum spanning subset in kpolymatroids. This algorithm has a performance ratio of approximately ln k, which is best possible for large k. A consequence of this algorithm is a polynomial time approximation algorithm with approximation ratio ln k for finding minimum weight spanning subhypergraphs in (k + 1)restricted hypergraphs. This generalization of the wellknown set cover problem naturally arises when computing Steiner minimum trees. Other applications of the algorithm include the rigidity problem in statics.
On Algorithmic Enumeration of HigherOrder
"... In the pursuit of realistic terrain models, Gudmundsson, Hammar, and van Kreveld introduced higherorder Delaunay triangulations. A usual Delaunay triangulation is a 0order Delaunay triangulation, thus unique for a nondegenerate point set, while orderk Delaunay triangulations can be nonunique wh ..."
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In the pursuit of realistic terrain models, Gudmundsson, Hammar, and van Kreveld introduced higherorder Delaunay triangulations. A usual Delaunay triangulation is a 0order Delaunay triangulation, thus unique for a nondegenerate point set, while orderk Delaunay triangulations can be nonunique when k ≥ 1. In this work, we propose an algorithm to list all orderk Delaunay triangulations of a given nondegenerate point set on the plane, when k ≤ 2, in polynomial time per triangulation. The main technique is the reverse search due to Avis and Fukuda, which exploits the connectedness of a certain graph over all objects to be listed. We also show that the same technique is unlikely to work for k ≥ 3 by exhibiting an example on which the associated graph is disconnected. 1
Results 1  10
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