Journal ArticleDOI
A fast algorithm for Steiner trees
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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 Article
Distributed Ant Colony QoS Multicast Routing Algorithm
Xu Hong,Wang Hua,YI Shan-wen +2 more
TL;DR: A distributed ant colony optimization algorithm is proposed that connects all the trees in the forest to form a single tree in a multicast tree’s forest during the ant movement progress.
Shrubbery: A New Algorithm for Quickly Growing High-Quality
TL;DR: Shrubbery as mentioned in this paper is an algorithm for solving the Steiner tree problem in deep sub-micron designs, which can consistently find optimal or near optimal solutions, but in less time than SPH.
Proceedings ArticleDOI
Routing Topology and Time-Division Multiplexing Co-Optimization for Multi-FPGA Systems
TL;DR: The proposed framework first generates high-quality topologies considering Net-Group criticalities, then, inspired by column generation, TDM ratio assignment is solved optimally by Lagrangian relaxation and outperforms the top three entries of ICCAD 2019 CAD Contest.
Journal ArticleDOI
Strategyproof auction mechanisms for network procurement
TL;DR: This work designs several deferred-acceptance auctions (DAAs) and compares their performance to the Vickrey–Clarke–Groves (VCG) mechanism as well as several other approximation mechanisms and observes that, even for medium-sized inputs, the VCG mechanisms experiences impractical runtimes and that the DAAs match the approximation ratios of even the best strategy-proof mechanisms in the average case.
Proceedings ArticleDOI
Shrubbery: a new algorithm for quickly growing high-quality Steiner trees
TL;DR: This paper presents a new algorithm, called "shrubbery", for solving the Steiner tree problem, and shows that shrubbery is able to consistently find optimal or near optimal solutions, but in less time than SPH.
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.