On the hop constrained steiner tree problem with multiple root nodes

Luis Gouveia*, Markus Leitner, Ivana Ljubić

*Corresponding author for this work

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review


We consider a new network design problem that generalizes the Hop and Diameter Constrained Minimum Spanning and Steiner Tree Problem as follows: given an edge-weighted undirected graph whose nodes are partitioned into a set of root nodes, a set of terminals and a set of potential Steiner nodes, find a minimum-weight subtree that spans all the roots and terminals so that the number of hops between each relevant node and an arbitrary root does not exceed a given hop limit H. The set of relevant nodes may be equal to the set of terminals, or to the union of terminals and root nodes. This paper presents theoretical and computational comparisons of flow-based vs. path-based mixed integer programming models for this problem. Disaggregation by roots is used to improve the quality of lower bounds of both models. To solve the problem to optimality, we implement branch-and-price algorithms for all proposed formulations. Our computational results show that the branch-and-price approaches based on path formulations outperform the flow formulations if the hop limit is not too loose.

Original languageEnglish
Title of host publicationCombinatorial Optimization - Second International Symposium, ISCO 2012, Revised Selected Papers
Number of pages12
Publication statusPublished - 27 Aug 2012
Externally publishedYes
Event2nd International Symposium on Combinatorial Optimization, ISCO 2012 - Athens, Greece
Duration: 19 Apr 201221 Apr 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7422 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference2nd International Symposium on Combinatorial Optimization, ISCO 2012


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