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Shortest-path tree

About: Shortest-path tree is a(n) research topic. Over the lifetime, 1584 publication(s) have been published within this topic receiving 32140 citation(s). more


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. more

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

1,111 Citations

Journal ArticleDOI: 10.1007/BF00288961
L. Kou1, George Markowsky1, L. Berman1Institutions (1)
01 Jun 1981-Acta Informatica
Abstract: Given an undirected distance graph G=(V, E, d) and a set S, where V is the set of vertices in G, E is the set of edges in G, d is a distance function which maps E into the set of nonnegative numbers and S?V is a subset of the vertices of V, the Steiner tree problem is to find a tree of G that spans S with minimal total distance on its edges. In this paper, we analyze a heuristic algorithm for the Steiner tree problem. The heuristic algorithm has a worst case time complexity of O(¦S¦¦V¦ 2) on a random access computer and it guarantees to output a tree that spans S with total distance on its edges no more than 2(1?1/l) times that of the optimal tree, where l is the number of leaves in the optimal tree. more

Topics: Steiner tree problem (69%), K-ary tree (67%), Spanning tree (66%) more

1,096 Citations

Open accessJournal ArticleDOI: 10.1109/90.993304
Abstract: Dynamic routing protocols such as RIP and OSPF essentially implement distributed algorithms for solving the shortest paths problem. The border gateway protocol (BGP) is currently the only interdomain routing protocol deployed in the Internet. BGP does not solve a shortest paths problem since any interdomain protocol is required to allow policy-based metrics to override distance-based metrics and enable autonomous systems to independently define their routing policies with little or no global coordination. It is then natural to ask if BGP can be viewed as a distributed algorithm for solving some fundamental problem. We introduce the stable paths problem and show that BGP can be viewed as a distributed algorithm for solving this problem. Unlike a shortest path tree, such a solution does not represent a global optimum, but rather an equilibrium point in which each node is assigned its local optimum. We study the stable paths problem using a derived structure called a dispute wheel, representing conflicting routing policies at various nodes. We show that if no dispute wheel can be constructed, then there exists a unique solution for the stable paths problem. We define the simple path vector protocol (SPVP), a distributed algorithm for solving the stable paths problem. SPVP is intended to capture the dynamic behavior of BGP at an abstract level. If SPVP converges, then the resulting state corresponds to a stable paths solution. If there is no solution, then SPVP always diverges. In fact, SPVP can even diverge when a solution exists. We show that SPVP will converge to the unique solution of an instance of the stable paths problem if no dispute wheel exists. more

  • Fig. 10. Illustration for Theorem V.4.
    Fig. 10. Illustration for Theorem V.4.
  • Fig. 8. Example of construction for clauseC = X _ X _ X .
    Fig. 8. Example of construction for clauseC = X _ X _ X .
  • Fig. 7. Variable assignment gadget forX .
    Fig. 7. Variable assignment gadget forX .
  • Fig. 12. The systemINCOHERENT.
    Fig. 12. The systemINCOHERENT.
  • Fig. 9. Dispute wheels.
    Fig. 9. Dispute wheels.
  • + 3

Topics: Border Gateway Protocol (57%), Open Shortest Path First (57%), Routing protocol (55%) more

519 Citations

Open accessJournal ArticleDOI: 10.1137/0214055
Greg N. Frederickson1Institutions (1)
Abstract: Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph. For the case of a general graph, mai... more

Topics: Spanning tree (73%), Minimum spanning tree (71%), Reverse-delete algorithm (67%) more

386 Citations

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Topic's top 5 most impactful authors

Balaji Raghavachari

12 papers, 525 citations

Guido Proietti

12 papers, 249 citations

Huynh Thi Thanh Binh

10 papers, 100 citations

Bang Ye Wu

10 papers, 185 citations

Neal E. Young

7 papers, 390 citations

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