Journal ArticleDOI
A fast algorithm for Steiner trees
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TLDR
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.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.read more
Citations
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Proceedings ArticleDOI
Polynomial algorithm for min-cost delay-constrained multicasting routing problem in networks
A.I. Erzin,Sang-Ha Kim +1 more
TL;DR: A novel polynomial algorithm is proposed for constructing a min-cost communication tree to connect the subset of network nodes which forms the multicast group of destinations in such way that the delays along each path from the source vertex to the sinks do not exceed the given delay bounds.
Journal ArticleDOI
A Survey of Multicasting in Optical Burst Switched Networks: Future Research Directions
TL;DR: The contributions of various researchers are studied thoroughly and compared to survey the various approaches and problems of multicasting in OBS networks and outline several future research directions in terms of applications in business, especially in Business- toBusiness (B2B) and Business-to-Consumer (B 2C) Models.
Book ChapterDOI
Source-Based minimum cost multicasting: intermediate-node selection with potentially low cost
TL;DR: A novel heuristic algorithm for constructing a minimum cost multicast tree based on a directed asymmetric network and shows an improvement in terms of network cost for general random topologies close to real networks.
Routing on the geometry of wireless ad hoc networks
TL;DR: The slotted programming paradigm that fosters modular programming and decouples unrelated software components temporally is described and it is shown that it is possible to forward messages greedily without ever falling in a local minimum.
References
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Journal ArticleDOI
A note on two problems in connexion with graphs
TL;DR: A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given.
Book ChapterDOI
Reducibility Among Combinatorial Problems
TL;DR: The work of Dantzig, Fulkerson, Hoffman, Edmonds, Lawler and other pioneers on network flows, matching and matroids acquainted me with the elegant and efficient algorithms that were sometimes possible.
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TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Journal ArticleDOI
Algorithm 97: Shortest path
TL;DR: The procedure was originally programmed in FORTRAN for the Control Data 160 desk-size computer and was limited to te t ra t ion because subroutine recursiveness in CONTROL Data 160 FORTRan has been held down to four levels in the interests of economy.
Journal ArticleDOI
Steiner Minimal Trees
E. N. Gilbert,H. O. Pollak +1 more
TL;DR: A Steiner minimal tree for given points in the plane is a tree which interconnects these points using lines of shortest possible total length as mentioned in this paper, where the length of the shortest possible line is chosen.