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Distributed minimum spanning tree

About: Distributed minimum spanning tree is a(n) research topic. Over the lifetime, 1717 publication(s) have been published within this topic receiving 39758 citation(s).

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Open accessJournal ArticleDOI: 10.1145/357195.357200
Abstract: Abstract : A distributed algorithm is presented that constructs the minimum weight 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 messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log of N to the base 2 + 2E and a message contains at most one edge weight plus log of 8N to the base 2 bits. The algorithm can be initiated spontaneously at any node or at any subset of nodes.

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Topics: Minimum spanning tree (86%), Spanning tree (81%), Distributed minimum spanning tree (78%) ...read more

1,111 Citations


ReportDOI: 10.21236/ADA080902
01 Oct 1979-
Abstract: : A distributed algorithm is presented that constructs the minimum weight 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 messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log of N to the base 2 + 2E and a message contains at most one edge weight plus log of 8N to the base 2 bits. The algorithm can be initiated spontaneously at any node or at any subset of nodes.

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Topics: Spanning tree (69%), Kruskal's algorithm (68%), Minimum spanning tree (67%) ...read more

1,059 Citations


Journal ArticleDOI: 10.1007/BF01584070
Michael Held1, Richard M. Karp2Institutions (2)
Abstract: The relationship between the symmetric traveling-salesman problem and the minimum spanning tree problem yields a sharp lower bound on the cost of an optimum tour. An efficient iterative method for approximating this bound closely from below is presented. A branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it, ranging in size up to sixty-four cities. The bounds used are so sharp that the search trees are minuscule compared to those normally encountered in combinatorial problems of this type.

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Topics: Combinatorial optimization (64%), Minimum spanning tree (63%), Spanning tree (60%) ...read more

1,009 Citations


Open accessProceedings ArticleDOI: 10.1109/INFCOM.2003.1209193
Ning Li1, Jennifer C. Hou1, Lui Sha1Institutions (1)
09 Jul 2003-
Abstract: In this paper, we present a minimum spanning tree (MST) based topology control algorithm, called local minimum spanning tree (LMST), for wireless multi-hop networks. In this algorithm, each node builds its local minimum spanning tree independently and only keeps on-tree nodes that are one-hop away as its neighbors in the final topology. We analytically prove several important properties of LMST: (1) the topology derived under LMST preserves the network connectivity; (2) the node degree of any node in the resulting topology is bounded by 6; and (3) the topology can be transformed into one with bidirectional links (without impairing the network connectivity) after removal of all uni-directional links. These results are corroborated in the simulation study.

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  • Fig. 1. A scenario that demonstrates that links in the topology derived under LMST may be uni-directional.
    Fig. 1. A scenario that demonstrates that links in the topology derived under LMST may be uni-directional.
  • TABLE I THE MAXIMUM, MINIMUM, AND AVERAGE DEGREES IN THE NETWORK TOPOLOGIES DERIVED USING THE MAXIMUM TRANSMISSION POWER, R&M(TWO-RAY GROUND MODEL), CBTC(5/6π), LMST, AND LMST WITH UNI-DIRECTIONAL LINKS REMOVED.
    TABLE I THE MAXIMUM, MINIMUM, AND AVERAGE DEGREES IN THE NETWORK TOPOLOGIES DERIVED USING THE MAXIMUM TRANSMISSION POWER, R&M(TWO-RAY GROUND MODEL), CBTC(5/6π), LMST, AND LMST WITH UNI-DIRECTIONAL LINKS REMOVED.
  • Fig. 4. Proof of Theorem 3.
    Fig. 4. Proof of Theorem 3.
  • Fig. 9. Performance comparisons (w.r.t. power consumption) between LMST (with uni-directional link removal) and R&M.
    Fig. 9. Performance comparisons (w.r.t. power consumption) between LMST (with uni-directional link removal) and R&M.
  • Fig. 5. Calculation of the probabilities that a new neighbor moves into the transmission range of a node and that an existing neighbor moves out of the transmission range, within a time interval of t.
    Fig. 5. Calculation of the probabilities that a new neighbor moves into the transmission range of a node and that an existing neighbor moves out of the transmission range, within a time interval of t.
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Topics: Minimum spanning tree (64%), Logical topology (63%), Distributed minimum spanning tree (63%) ...read more

826 Citations


Journal ArticleDOI: 10.1109/MAHC.1985.10011
Abstract: It is standard practice among authors discussing the minimum spanning tree problem to refer to the work of Kruskal(1956) and Prim (1957) as the sources of the problem and its first efficient solutions, despite the citation by both of Boruvka (1926) as a predecessor. In fact, there are several apparently independent sources and algorithmic solutions of the problem. They have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century. We shall explore and compare these works and their motivations, and relate them to the most recent advances on the minimum spanning tree problem.

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Topics: Minimum spanning tree (66%), Spanning tree (63%), Distributed minimum spanning tree (62%) ...read more

714 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20202
20193
201812
201745
201662
201577

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Topic's top 5 most impactful authors

Gustavo Bergantiños

13 papers, 317 citations

Juan Vidal-Puga

11 papers, 286 citations

David Peleg

10 papers, 605 citations

Stephane Rovedakis

9 papers, 153 citations

Lélia Blin

8 papers, 111 citations

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