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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Journal ArticleDOI
QoS Constraints Multicast Routing for Residual Bandwidth Optimization using Evolutionary Algorithm
Sushma Jain,Jaydev Sharma +1 more
TL;DR: An approach based on an evolutionary algorithm to solve the QoS constraint multicast routing problem is presented, which maximizes residual bandwidth utilization while satisfying end-to-end delay and delay jitter bounds.
Book ChapterDOI
Accelerated Steiner Tree Problem Solving on GPU with CUDA
TL;DR: The first parallel heuristics for the solution of the STPG for GPU with CUDA are presented, and it is shown that the achieved speedups for different kinds of graphs are significant compared to one of the fastest serial heuristic STAR.
Proceedings ArticleDOI
A bi-criteria algorithm for multipoint-to-multipoint virtual connections in transport networks
TL;DR: In this work a heuristic was developed based on a known bi-criteria spanning tree algorithm that finds the set of efficient supported solutions in a given sub-graph that allows to obtain ‘good’ compromise Steiner trees in an efficient manner.
Journal ArticleDOI
RAD: Recipient-anonymous data delivery based on public routing proxies
Hyoungshick Kim,Jaehoon Jeong +1 more
TL;DR: This paper presents a Recipient-Anonymous DataDelivery (RAD), tailored and optimized for stable-topology networks and demonstrates the practicality of the proposed protocol through intensive simulation based on well-known network topologies.
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.
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.