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Linear Programming in the Semistreaming Model with Application to the Maximum Matching Problem
, 2012
"... In this paper we study linearprogramming based approaches to the maximum matching problem in the semistreaming model. In this model edges are presented sequentially, possibly in an adversarial order, and we are only allowed to use a small space. The allowed space is near linear in the number of ve ..."
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Cited by 5 (1 self)
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In this paper we study linearprogramming based approaches to the maximum matching problem in the semistreaming model. In this model edges are presented sequentially, possibly in an adversarial order, and we are only allowed to use a small space. The allowed space is near linear in the number of vertices (and sublinear in the number of edges) of the input graph. The semistreaming model is relevant in the context of processing of very large graphs. In recent years, there have been several new and exciting results in the semistreaming model. However broad techniques such as linear programming have not been adapted to this model. In this paper we present several techniques to adapt and optimize linearprogramming based approaches in the semistreaming model. We use the maximum matching problem as a foil to demonstrate the e ectiveness of adapting such tools in this model. As a consequence we improve almost all previous results on the semistreaming maximum matching problem. We also prove new results on interesting variants.
New Sublinear Methods in the Struggle against Classical Problems
, 2010
"... We study the time and query complexity of approximation algorithms that access only a minuscule fraction of the input, focusing on two classical sources of problems: combinatorial graph optimization and manipulation of strings. The tools we develop find applications outside of the area of sublinear ..."
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Cited by 2 (0 self)
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We study the time and query complexity of approximation algorithms that access only a minuscule fraction of the input, focusing on two classical sources of problems: combinatorial graph optimization and manipulation of strings. The tools we develop find applications outside of the area of sublinear algorithms. For instance, we obtain a more efficient approximation algorithm for edit distance and distributed algorithms for combinatorial problems on graphs that run in a constant number of communication rounds.
A Simple Parallel Approximation Algorithm for the Weighted Matching Problem
, 2007
"... Given a weighted graph, the weighted matching problem is to find a matching with maximum weight. The fastest known exact algorithm runs in O(nm + n2 log n) however for many real world applications this is too costly, and an approximate matching is sufficient. A capproximation algorithm is one which ..."
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Given a weighted graph, the weighted matching problem is to find a matching with maximum weight. The fastest known exact algorithm runs in O(nm + n2 log n) however for many real world applications this is too costly, and an approximate matching is sufficient. A capproximation algorithm is one which always finds a weight of at least c times the optimal weight. Drake and Hougardy developed a linear time 2/3  epsilon approximation algorithm which is the best known serial algorithm. They also developed a parallel 1 epsilon approximation algorithm for the PRAM model, however it requires a large number of processors which is not as useful in practice. Hoepman developed a distributed 1/2 approximation algorithm which is the best known distributed algorithm. We present a shared memory parallel version of the best 2/3  epsilon algorithm, which is simple to understand and easy to implement.