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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Book ChapterDOI
Steiner Tree 1.39-Approximation in Practice
Stephan Beyer,Markus Chimani +1 more
TL;DR: This work first solves a hypergraphic LP relaxation and then applies matroid theory to obtain an integral solution and considers the currently strongest Steiner tree approximation algorithm, published by Goemans, Olver, Rothvos and Zenklusen (2012).
Analytical models for accelerating FPGA architecture development
TL;DR: This dissertation develops models that relate key FPGA architectural parameters to the depth along the critical path and the post-placement wirelength and details how these models can be used to estimate the expected area of implementation and critical path delay for user-cir cuits mapped on FPGAs.
Proceedings ArticleDOI
Constructing minimum cost dynamic multicast trees under delay constraint
M. Yang,Yuanyuan Yang +1 more
TL;DR: A heuristic algorithm which can construct a delay constrained minimum cost multicast tree dynamically and can add or remove a group number without rerouting the path between the source and other group members is designed.
Journal Article
Left ventricle tracking in isotopic ventriculography using statistical deformable models
TL;DR: The article focuses on the implementation of genetic multicast algorithms in ad-hoc networks and proposes a new approach in adhoc network modelling.
Proceedings ArticleDOI
Efficient algorithms for multiple destinations routing
TL;DR: Simulation on two example networks shows that all three heuristics designed for connecting a large number of nodes in the network give better solutions (or lower-cost connection paths) than the improved RS algorithm.
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.