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
A Network-Flow Based Influence Propagation Model for Social Networks
TL;DR: The minimum cost flow model effectively propagates influences to neighbouring nodes with minimum costs in each path of the social network, removing noise associated with social network marketing information and propagating influences without overlapping in information nodes.
Journal ArticleDOI
Modelling Multicast QoS Routing by using Best-Tree Search in And-or Graphs and Soft Constraint Logic Programming
TL;DR: The semantics of an SCLP program computes the best tree in the corresp onding and-or graph, and this result can be adopted to find, from a given source node, the multicast distribution tree having minimum cost and all the destination nodes of the multicasts communication.
Proceedings ArticleDOI
Multicast flow routing: Evaluation of heuristics and multiobjective evolutionary algorithms
TL;DR: Two heuristics for subtree reconnection are investigated, applicable in crossover and mutation operators, and results indicate that SPEA2 overcame SPEA and NSGA-II, besides providing the best combination with one the heuristic, obtaining the best average results.
Book ChapterDOI
Minimum Steiner Tree Construction.
TL;DR: This chapter addresses several variations of the corresponding fundamental Steiner minimal tree (SMT) problem, where a given set of pins is to be connected using minimum total wirelength.
Book ChapterDOI
Two Constant Approximation Algorithms for Node-Weighted Steiner Tree in Unit Disk Graphs
TL;DR: This paper shows that for unit disk graph, the node-weighted Steiner tree problem is still NP-hard, however it has polynomial time constant approximation, and obtains that there is polynometric time (9.875+?)-approximation algorithm for minimum weight connected dominating set in unit disk graphs.
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
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Reducibility Among Combinatorial Problems.
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.