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A general approximation technique for constrained forest problems
 in Proceedings of the 3rd Annual ACMSIAM Symposium on Discrete Algorithms
, 1992
"... Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimizatio ..."
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Cited by 355 (21 self)
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Abstract. We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 123 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
Computing cycle covers without short cycles
 In Proc. 9th Ann. European Symp. on Algorithms (ESA)
, 2001
"... A cycle cover of a graph is a spanning subgraph where each node is part of exactly one simple cycle. A kcycle cover is a cycle cover where each cycle has length at least k. We call the decision problems whether a directed or undirected graph has a kcycle cover kDCC and kUCC. Given a graph with e ..."
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Cited by 20 (5 self)
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A cycle cover of a graph is a spanning subgraph where each node is part of exactly one simple cycle. A kcycle cover is a cycle cover where each cycle has length at least k. We call the decision problems whether a directed or undirected graph has a kcycle cover kDCC and kUCC. Given a graph with edge weights one and two, MinkDCC and MinkUCC are the minimization problems of finding a kcycle cover with minimum weight. We present factor 4=3 approximation algorithms for MinkDCC with running time O(n