Bounded-degree spanning tree problems: models and new algorithms

Authors:
R. Cerulli;M. Gentili;A. Iossa
Affiliations:
Dipartimento di Matematica ed Informatica, Università di Salerno, Fisciano (SA), Italy 84084;Dipartimento di Matematica ed Informatica, Università di Salerno, Fisciano (SA), Italy 84084;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università degli studi di Roma "La Sapienza", Rome (RM), Italy 00185
Venue:
Computational Optimization and Applications
Year:
2009

Citing 2
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A nearly best-possible approximation algorithm for node-weighted Steiner trees

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Spanning Trees with Bounded Number of Branch Vertices

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming

An iterative refinement algorithm for the minimum branch vertices problem

SEA'11 Proceedings of the 10th international conference on Experimental algorithms
New heuristics for two bounded-degree spanning tree problems

Information Sciences: an International Journal
Lower and upper bounds for the spanning tree with minimum branch vertices

Computational Optimization and Applications

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Abstract

Given a connected graph G, a vertex v of G is said to be a branch vertex if its degree is greater than 2. We consider two problems arising in the context of optical networks: Finding a spanning tree of G with the minimum number of branch vertices and Finding a spanning tree of G such that the degree sum of the branch vertices is minimized. For these NP-hard problems, heuristics, that give good quality solutions, do not exist in the literature. In this paper we analyze the relation between the problems, provide a single commodity flow formulation to solve the problems by means of a solver and develop different heuristic strategies to compute feasible solutions that are compared with the exact ones. Our extensive computational results show the algorithms to be very fast and effective.