Approximability of Connected Factors

Kamiel Cornelissen, R.P. Hoeksma, Bodo Manthey, N.S. Narayanaswamy, C.S. Rahul

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

6 Citations (Scopus)
1 Downloads (Pure)


Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte’s reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard – finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected d-factor. We give a 3-approximation for all d and improve this to an (r + 1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r + 1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.
Original languageUndefined
Title of host publicationProceedings of the 11th Workshop on Approximation and Online Algorithms (WAOA 2013)
EditorsC. Kaklamanis, K. Pruhs
Place of PublicationBerlin, Germany
Number of pages12
ISBN (Print)978-3-319-08000-0
Publication statusPublished - 2014
Event11th Workshop on Approximation and Online Algorithms 2013 - Sophia Antipolis, France
Duration: 5 Sept 20136 Sept 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer International Publishing
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th Workshop on Approximation and Online Algorithms 2013
Abbreviated titleWAOA 2013
CitySophia Antipolis
Internet address


  • EWI-24832
  • Graph factors
  • METIS-305910
  • Approximation algorithms
  • IR-91426

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