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
Optimally cutting a surface into a disk
Jeff Erickson,Sariel Har-Peled +1 more
TL;DR: It is shown that the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk is NP-hard, even for manifolds without boundary and for punctured spheres.
Journal ArticleDOI
The Steiner problem in distributed computing systems
TL;DR: A distributed algorithm is presented for constructing a nearly optimal Steiner tree in an asynchronous network represented by a weighted communication graph G = (V, E, c) where G is the subset of nodes of G to be connected.
Proceedings ArticleDOI
An efficient multicast routing algorithm for delay-sensitive applications with dynamic membership
TL;DR: An algorithm for finding a multicast tree in packet-switched networks based on the minimum cost Steiner tree problem and utilizing an optimization technique called Lagrangian relaxation method which can find near-optimal multicast trees.
Journal ArticleDOI
Spectrum and Energy Efficient Relay Station Placement in Cognitive Radio Networks
TL;DR: This paper designs a framework of heuristic algorithms to compute the near-optimal solutions for cost minimization in cognitive radio networks and shows that the proposed algorithms outperform the random placement strategy and the number of required RSs obtained by the algorithms is always within 2 times of that in the optimal solution.
Journal ArticleDOI
Combinatorial optimization in system configuration design
TL;DR: Several system configuration problems are investigated andbinatorial optimization models (including multicriteria statements) are under examination: multiple choice problem, allocation problem, graph coloring problems, morphological clique problem (with compatibility of system components), multipartite clique and their modifications, spanning trees problems.
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.