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Optimal File Sharing in Distributed Networks
, 1991
"... The following le distribution problem is considered: Given a network of processors represented by an undirected graph G = (V; E), and a le size k, an arbitrary le 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 mem ..."
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Cited by 32 (2 self)
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The following le distribution problem is considered: Given a network of processors represented by an undirected graph G = (V; E), and a le size k, an arbitrary le 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 le distribution scheme which realizes this objective for k log G, where 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 le w into the node memory devices, can be computed in time complexity which is polynomial in k and jV j. Furthermore, each node can reconstruct the contents of such a le w in O(k 2) bit operations. Finally, it is shown that the requirement of k being much larger than log G is necessary in order to have total memory size close to the integer programming lower bound.
A Unified Local Ratio Approximation of NodeDeletion Problems (Extended Abstract)
 PROC. 4TH EUROPEAN SYMP. ON ALGORITHMS
, 1996
"... In this paper we consider a unified approximation method for nodedeletion problems with nontrivial and hereditary graph properties. It was proved 16 years ago that every nodedeletion problems for a nontrivial hereditary property is NPcomplete via a few generic approximation preserving reducti ..."
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In this paper we consider a unified approximation method for nodedeletion problems with nontrivial and hereditary graph properties. It was proved 16 years ago that every nodedeletion problems for a nontrivial hereditary property is NPcomplete via a few generic approximation preserving reductions from the Vertex Cover problem. An open problem posed at that time is concerned with the other direction of approximability: can other nodedeletion problems be approximated as good as the Vertex Cover ? The goal of the current paper is to take a first step along the direction of research suggested above. More specifically, one generic approximation algorithm is presented, which is applicable to every nodedeletion problem for a hereditary property. It will be seen then that under simple and na...