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Parallelized approximation algorithms for minimum routing cost spanning trees
, 2008
"... Let G = (V, E) be an undirected graph with a nonnegative edgeweight function w. The routing cost of a spanning tree T of G is ∑ u,v∈V dT (u, v), where dT (u, v) denotes the weight of the simple uv path in T. The Minimum Routing Cost Spanning Tree (MRCT) problem [WLB+ 00] asks for a spanning tree o ..."
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of G with the minimum routing cost. In this paper, we parallelize several previously proposed approximation algorithms for the MRCT problem and some of its variants. Let ɛ> 0 be an arbitrary constant. When the edgeweight function w is given in unary, we parallelize the (4/3 + ɛ)approximation
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... 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 proble ..."
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Cited by 409 (21 self)
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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
Polynomial time approximation schemes for Euclidean Traveling Salesman and other geometric problems
, 1998
"... We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes are in � ..."
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Cited by 390 (2 self)
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to Christofides) achieves a 3/2approximation in polynomial time. We also give similar approximation schemes for some other NPhard Euclidean problems: Minimum Steiner Tree, kTSP, and kMST. (The running times of the algorithm for kTSP and kMST involve an additional multiplicative factor k.) The previous best
A Polynomial Time Approximation Scheme for Minimum Routing Cost Spanning Trees
"... Given an undirected graph with nonnegative costs on the edges, the routing cost of any of its spanning trees is the sum over all pairs of vertices of the cost of the path between the pair in the tree. Finding a spanning tree of minimum routing cost is NPhard, even when the costs obey the triangle i ..."
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inequality. We show that the general case is in fact reducible to the metric case and present a polynomialtime approximation scheme valid for both versions of the problem. In particulaf, we show how to build a spanning tree of an nvertex weighted graph with routing cost within (1 + E) from the minimum
CommunicationOptimal Parallel Minimum Spanning Tree Algorithms
, 1998
"... Lower and upper bounds for finding a minimum spanning tree (MST) in a weighted undirected graph on the BSP model are presented. We provide the first nontrivial lower bounds on the communication volume required to solve the MST problem. Let p denote the number of processors, n the number of nodes of ..."
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Cited by 13 (1 self)
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Lower and upper bounds for finding a minimum spanning tree (MST) in a weighted undirected graph on the BSP model are presented. We provide the first nontrivial lower bounds on the communication volume required to solve the MST problem. Let p denote the number of processors, n the number of nodes
Distributed Approximation of Minimum Routing Cost Trees∗
, 2014
"... We study the NPhard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph G over n nodes that minimizes the sum of distances between all pairs of nodes. In the c ..."
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We study the NPhard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph G over n nodes that minimizes the sum of distances between all pairs of nodes
A polynomialtime approximation scheme for minimum routing cost spanning trees
 SIAM J. COMPUT
, 1999
"... Given an undirected graph with nonnegative costs on the edges, the routing cost of any of its spanning trees is the sum over all pairs of vertices of the cost of the path between the pair in the tree. Finding a spanning tree of minimum routing cost is NPhard, even when the costs obey the triangle ..."
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Cited by 21 (2 self)
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inequality. We show that the general case is in fact reducible to the metric case and present a polynomialtime approximation scheme valid for both versions of the problem. In particular, we show how to build a spanning tree of an nvertex weighted graph with routing cost at most (1 + ɛ) of the minimum
Applying parallel computation algorithms in the design of serial algorithms
 J. ACM
, 1983
"... The goal of this paper is to point out that analyses of parallelism in computational problems have practical implications even when multiprocessor machines are not available. This is true because, in many cases, a good parallel algorithm for one problem may turn out to be useful for designing an eff ..."
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Cited by 241 (7 self)
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an efficient serial algorithm for another problem. A d ~ eframework d for cases like this is presented. Particular cases, which are discussed in this paper, provide motivation for examining parallelism in sorting, selection, minimumspanningtree, shortest route, maxflow, and matrix multiplication problems
Practical Parallel Algorithms for Minimum Spanning Trees
 In Workshop on Advances in Parallel and Distributed Systems
, 1998
"... We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns ..."
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Cited by 21 (0 self)
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We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns
Results 1  10
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