A fast algorithm for Steiner trees

Kou, Lawrence T.; Markowsky, George; Berman, Leonard

doi:10.1007/bf00288961

Cited by 1,018 publications

(553 citation statements)

References 9 publications

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“…In MCT [2], minimum cost path between any two nodes are first computed. These paths make up the links of a minimum cost graph.…”

Section: Minimum Cost Tree Heuristic (Mct)mentioning

confidence: 99%

“…Pruning may be required to remove any unnecessary links. It has been shown in [2] that MCT is able to obtain trees with cost very close to the optimal. Thus, we evaluate the performance of our proposed algorithm using MCT as the benchmark in terms of cost efficiency.…”

Section: Minimum Cost Tree Heuristic (Mct)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The most well-known is the one from [2] which constructs minimum cost tree for each multicast-session from a graph consisting of minimum cost paths between any two nodes for all the nodes. We henceforth refer the heuristic from [2] as Minimum Cost Tree heuristic (MCT). As MCT or any other source-based algorithms constructs a tree for each session from source to its destinations, the overheads incurred and the time to construct a tree will be large if the number of destinations is large.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Heuristic for Minimum Cost Trees Construction in Multi-Groups Multicast

Yong

Poo

Cheng

2008

NETWORKING 2008 Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet

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Abstract. We propose an efficient and fast heuristic algorithm (MGST) to construct minimum cost tree for each multicast-group in multi-groups multicast. The idea is to construct just one spanning shared-tree that allows minimum cost tree of each multicast-group to be computed from this shared-tree. MGST is compared with the low overheads Core-Based Tree algorithm (CBT) and approximate optimal cost Minimum Cost Tree heuristic (MCT) through simulations. The results showed that MGST constructs trees with average cost close to the approximate optimal (7% difference). The overheads incurred from MGST are also comparable to CBT and much lesser than MCT. In addition, MGST has also shown to construct minimum cost trees much faster than MCT and comparable to CBT. To further improve the performance, "trace back" method is introduced to MGST and denoted as MGST-T. MGST-T yields average cost performance of only 2% difference from the optimal and with almost the same overheads and trees' construction time as MGST.

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“…In MCT [2], minimum cost path between any two nodes are first computed. These paths make up the links of a minimum cost graph.…”

Section: Minimum Cost Tree Heuristic (Mct)mentioning

confidence: 99%

Section: Minimum Cost Tree Heuristic (Mct)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Heuristic for Minimum Cost Trees Construction in Multi-Groups Multicast

Yong

Poo

Cheng

2008

NETWORKING 2008 Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet

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“…Various types of the approximate algorithms for the Steiner tree problems have previously been proposed [8][9][10]. Among these, the KMB algorithm [2] is an effective method for obtaining shorter Steiner trees. However, the KMB algorithm obtains various patterns of Steiner trees, and sometimes a Steiner tree is obtained at a very high cost.…”

Section: Introductionmentioning

confidence: 99%

An Effective Construction Algorithm for the Steiner Tree Problem Based on Edge Betweenness

Kimura

Jin’no

2016

Journal of Signal Processing

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Given an undirected weighted graph G = (V, E, c) and a set T , where V is the set of nodes, E is the set of edges, c is a cost function, and T is a subset of nodes called terminals, the Steiner tree problem in graphs is that of finding the subgraph of the minimum weight that connects all of terminals.The Steiner tree problem is an example of an NP-complete combinatorial optimization problem [1]. Thus, approximate methods are usually employed for constructing the Steiner tree. In this study, the KMB algorithm [2], which is an efficient construction method for Steiner tree problems, is enhanced by considering edge betweenness [3]. The results of numerical simulations indicate that our improved KMB algorithm shows good performances for various types of benchmark Steiner tree problems.

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Efficient multicast design in a microkernel environment

Averbuch

Cohen

1998

Concurrency: Pract. Exper.

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A fast algorithm for Steiner trees

Cited by 1,018 publications

References 9 publications

Efficient Heuristic for Minimum Cost Trees Construction in Multi-Groups Multicast

Efficient Heuristic for Minimum Cost Trees Construction in Multi-Groups Multicast

An Effective Construction Algorithm for the Steiner Tree Problem Based on Edge Betweenness

Efficient multicast design in a microkernel environment

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