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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].
Efficient probabilistically checkable proofs and applications to approximation
 In Proceedings of STOC93
, 1993
"... 1 ..."
Optimal File Sharing in Distributed Networks
 SIAM J. Comput
, 1991
"... The following file distribution problem is considered: Given a network of processors represented by an undirected graph G = (V; E), and a file size k, an arbitrary file w of k bits is to be distributed among all nodes of G. To this end, each node is assigned a memory device such that, by accessing t ..."
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Cited by 23 (1 self)
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The following file distribution problem is considered: Given a network of processors represented by an undirected graph G = (V; E), and a file size k, an arbitrary file w of k bits is to be distributed among all nodes of G. To this end, each node is assigned a memory device such that, by accessing the memory of its own and of its adjacent nodes, the node can reconstruct the contents of w. The objective is to minimize the total size of memory in the network. This paper presents a file distribution scheme which realizes this objective for k AE log \Delta G , where \Delta G stands for the maximum degree in G: For this range of k, the total memory size required by the suggested scheme approaches an integer programming lower bound on that size. The scheme is also constructive in the sense that, given G and k, the memory size at each node in G, as well as the mapping of any file w into the node memory devices, can be computed in time complexity which is polynomial in k and jV j. Furthermore...
NoiseTolerant DistributionFree Learning of General Geometric Concepts
, 1996
"... this paper. First, we give an algorithm to learn C ..."
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Cited by 16 (3 self)
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this paper. First, we give an algorithm to learn C