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
Survivable networks, linear programming relaxations and the parsimonious property
TL;DR: This work establishes a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the survivable network design problem, and derives various structural properties of these LP relaxations.
Journal ArticleDOI
A survey of community search over big graphs
TL;DR: A comprehensive review of existing community search works can be found in this paper, where the authors analyze and compare the quality of communities under their models, and the performance of different solutions.
Proceedings ArticleDOI
Multicasting for multimedia applications
TL;DR: The authors investigate multicast routing for high-bandwidth delay-sensitive applications in a point-to-point network as an optimization problem and present an efficient approximation algorithm.
Journal ArticleDOI
Multicast tree generation in networks with asymmetric links
TL;DR: In this article, a polynomial-time algorithm that provides for trade-off selection, using a single parameter /spl kappa/, between the tree-cost (Steiner cost) and the run time efficiency, is presented.
Journal ArticleDOI
Constrained relay node placement in wireless sensor networks: formulation and approximations
TL;DR: Constrained versions of the relay node placement problem, where relay nodes can only be placed at a set of candidate locations, are studied and a framework of polynomial time O(1) -approximation algorithms with small approximation ratios is presented.
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.