article

The 2-hop spanning tree problem

Author:

Geir DahlAuthors Info & Claims

Operations Research Letters, Volume 23, Issue 1-2

Pages 21 - 26

https://doi.org/10.1016/S0167-6377(98)00029-7

Published: 01 August 1998 Publication History

Abstract

A spanning tree in a graph G where each node has distance at most 2 from a root node r is called a 2-hop spanning tree. For given edge weights the 2-hop spanning tree problem is to find a minimum weight 2-hop spanning tree. The problem is NP-hard. We study the problem from a polyhedral point of view based on a directed formulation and give, for example, a completeness result when G is an n-wheel.

References

[1]

T.S. Arthanari, Y. Dodge, Mathematical Programming in Statistics, Wiley, New York, 1986.

Google Scholar

[2]

G. Dahl, Stable set polytopes for a class of circulant graphs, University of Oslo, Institute of Informatics, Report 249, May 1997 (to appear in SIAM Optimization).

Google Scholar

[3]

L. Gouveia, Using variable redefinition for computing minimum spanning and Steiner trees with hop constraints, Faculdade de Ciéncias da Universidade de Lisboa, Centro de investigação operacional, Lisboa, Portugal, Report 2, 1996.

Google Scholar

[4]

T.L. Magnanti, L.A. Wolsey, Optimal trees, in: Ball et al. (Eds.), Network Optimization, Handbooks in Operations Research and Management Science, vol. 7, North-Holland, Amsterdam, 1995, pp. 503-615.

Google Scholar

[5]

G. Nemhauser, L.A. Wolsey, Integer and Combinatorial Optimization, Wiley, New York, 1988.

Crossref

Google Scholar

Cited By

View all

Yao PGuo L(2022)Exact algorithms for finding constrained minimum spanning treesJournal of Combinatorial Optimization10.1007/s10878-020-00579-z44:3(2085-2103)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10878-020-00579-z
Yao PGuo L(2017)Fast Approximation Algorithms for Computing Constrained Minimum Spanning TreesCombinatorial Optimization and Applications10.1007/978-3-319-71150-8_9(103-110)Online publication date: 16-Dec-2017
https://dl.acm.org/doi/10.1007/978-3-319-71150-8_9
(2016)Layered graph models and exact algorithms for the generalized hop-constrained minimum spanning tree problemComputers and Operations Research10.1016/j.cor.2015.06.01265:C(1-18)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.cor.2015.06.012
Show More Cited By

The 2-hop spanning tree problem
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
  2. Mathematical analysis
    1. Mathematical optimization
      1. Continuous optimization
      2. Mixed discrete-continuous optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
      1. Mixed discrete-continuous optimization

Recommendations

An exact algorithm for the maximum leaf spanning tree problem

Given a connected graph, the Maximum Leaf Spanning Tree Problem (MLSTP) is to find a spanning tree whose number of leaves (degree-one vertices) is maximum. We propose a branch-and-bound algorithm for MLSTP, in which an upper bound is obtained by solving ...
Min-degree constrained minimum spanning tree problem with fixed centrals and terminals

A variant of the Min-Degree Constrained Minimum Spanning Tree Problem is proposed.Each node is fixed as central (with a minimum degree constraint) or terminal (leaf).The feasibility problem is shown to be NP-Complete.Necessary and sufficient conditions ...
The maximum-leaf spanning tree problem: Formulations and facets

The Maximum Leaf Spanning Tree Problem (MLSTP) is to find a spanning tree in a given undirected graph, whose number of leaves (vertices of degree 1) is maximum. In this article, we consider an integer programming approach to the MLSTP. We provide two ...

Comments

Information & Contributors

Information

Published In

Operations Research Letters Volume 23, Issue 1-2

August, 1998

63 pages

ISSN:0167-6377

Issue’s Table of Contents

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 August 1998

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 06 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Yao PGuo L(2022)Exact algorithms for finding constrained minimum spanning treesJournal of Combinatorial Optimization10.1007/s10878-020-00579-z44:3(2085-2103)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10878-020-00579-z
Yao PGuo L(2017)Fast Approximation Algorithms for Computing Constrained Minimum Spanning TreesCombinatorial Optimization and Applications10.1007/978-3-319-71150-8_9(103-110)Online publication date: 16-Dec-2017
https://dl.acm.org/doi/10.1007/978-3-319-71150-8_9
(2016)Layered graph models and exact algorithms for the generalized hop-constrained minimum spanning tree problemComputers and Operations Research10.1016/j.cor.2015.06.01265:C(1-18)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.cor.2015.06.012
Diarrassouba IGabrel VMahjoub AGouveia LPesneau P(2016)Integer programming formulations for the k-edge-connected 3-hop-constrained network design problemNetworks10.1002/net.2166767:2(148-169)Online publication date: 1-Mar-2016
https://dl.acm.org/doi/10.1002/net.21667
Escoffier BGourvès LMonnot J(2013)Fair solutions for some multiagent optimization problemsAutonomous Agents and Multi-Agent Systems10.1007/s10458-011-9188-z26:2(184-201)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1007/s10458-011-9188-z
Gouveia LPaias ASharma D(2011)Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problemJournal of Heuristics10.1007/s10732-009-9123-517:1(23-37)Online publication date: 1-Feb-2011
https://dl.acm.org/doi/10.1007/s10732-009-9123-5
Gouveia LSimonetti LUchoa E(2011)Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphsMathematical Programming: Series A and B10.1007/s10107-009-0297-2128:1-2(123-148)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1007/s10107-009-0297-2
Hassin RLevin A(2003)Minimum spanning tree with hop restrictionsJournal of Algorithms10.1016/S0196-6774(03)00051-848:1(220-238)Online publication date: 1-Aug-2003
https://dl.acm.org/doi/10.1016/S0196-6774%2803%2900051-8

Abstract

References

Cited By

Recommendations

An exact algorithm for the maximum leaf spanning tree problem

Min-degree constrained minimum spanning tree problem with fixed centrals and terminals

The maximum-leaf spanning tree problem: Formulations and facets

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Share

Share this Publication link

Share on social media

Affiliations