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A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 435 (3 self)
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A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm
Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
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Cited by 739 (18 self)
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matching), improved from O(nm log0dn+2)n); (4) O(mj3(m, n)) for the minimum spanning tree problem, improved from O(mloglo&,,.+2,n), where j3(m, n) = min {i 1 log % 5 m/n). Note that B(m, n) 5 log*n if m 2 n. Of these results, the improved bound for minimum spanning trees is the most striking, although
Multicast Routing in Datagram Internetworks and Extended LANs
 ACM Transactions on Computer Systems
, 1990
"... Multicasting, the transmission of a packet to a group of hosts, is an important service for improving the efficiency and robustness of distributed systems and applications. Although multicast capability is available and widely used in local area networks, when those LANs are interconnected by store ..."
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Cited by 1074 (5 self)
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describe modifications to the singlespanningtree routing algorithm commonly used by linklayer bridges, to reduce the costs of multicasting in large extended LANs. Finally, we discuss how the use of multicast scope control and hierarchical multicast routing allows the multicast service to scale up
A Data Structure for Dynamic Trees
, 1983
"... A data structure is proposed to maintain a collection of vertexdisjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) ti ..."
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Cited by 347 (21 self)
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trees. (4) Implementing the network simplex algorithm for minimumcost flows. The most significant application is (2); an O(mn log n)time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse
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 414 (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
Submodularity of MinimumCost Spanning Tree
"... We give a necessary condition and a sufficient condition for a minimumcost spanning tree game introduced by Bird to be submodular (or convex). When the cost is restricted to two values, we give a characterization of submodular minimumcost spanning tree games. We also discuss algorithmic issues. ..."
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We give a necessary condition and a sufficient condition for a minimumcost spanning tree game introduced by Bird to be submodular (or convex). When the cost is restricted to two values, we give a characterization of submodular minimumcost spanning tree games. We also discuss algorithmic issues.
Minimum Cost Spanning Tree Games
, 2001
"... most grateful to two anonymous referees and an Associate Editor for remarkably detailed comments on an earlier version of the paper. We also acknowledge helpful suggestions from A.van den Nouweland and H. Moulin. We propose a new cost allocation rule for minimum cost spanning tree games. The new rul ..."
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most grateful to two anonymous referees and an Associate Editor for remarkably detailed comments on an earlier version of the paper. We also acknowledge helpful suggestions from A.van den Nouweland and H. Moulin. We propose a new cost allocation rule for minimum cost spanning tree games. The new
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
 Journal of the ACM
, 1998
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c Ͼ 1 and given any n nodes in 2 , a randomized version of the scheme finds a (1 ϩ 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes ..."
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Cited by 397 (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
On constructing minimum spanning trees in kdimensional space and related problems
 SIAM JOURNAL ON COMPUTING
, 1982
"... . The problem of finding a minimum spanning tree connecting n points in a kdimensional space is discussed under three common distance metrics: Euclidean, rectilinear, and L. By employing a subroutine that solves the post office problem, we show that, for fixed k _> 3, such a minimum spanning t ..."
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Cited by 222 (1 self)
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. The problem of finding a minimum spanning tree connecting n points in a kdimensional space is discussed under three common distance metrics: Euclidean, rectilinear, and L. By employing a subroutine that solves the post office problem, we show that, for fixed k _> 3, such a minimum spanning
Minimum Bounded Degree Spanning Trees
, 2006
"... We consider the minimum cost spanning tree problem under the restriction that all degrees must be at most a given value k. We show that we can efficiently find a spanning tree of maximum degree at most k + 2 whose cost is at most the cost of the optimum spanning tree of maximum degree at most k. Thi ..."
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Cited by 43 (0 self)
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We consider the minimum cost spanning tree problem under the restriction that all degrees must be at most a given value k. We show that we can efficiently find a spanning tree of maximum degree at most k + 2 whose cost is at most the cost of the optimum spanning tree of maximum degree at most k
Results 1  10
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