article

On the approximability of some degree-constrained subgraph problems

Authors:

Stéphane Pérennes,

Saket SaurabhAuthors Info & Claims

Discrete Applied Mathematics, Volume 160, Issue 12

Pages 1661 - 1679

https://doi.org/10.1016/j.dam.2012.03.025

Published: 01 August 2012 Publication History

Abstract

In this article we provide hardness results and approximation algorithms for the following three natural degree-constrained subgraph problems, which take as input an undirected graph G=(V,E). Let d>=2 be a fixed integer. The Maximumd-degree-bounded Connected Subgraph (MDBCS"d) problem takes as additional input a weight function @w:E->R^+, and asks for a subset E^'@?E such that the subgraph induced by E^' is connected, has maximum degree at most d, and @?"e"@?"E"^"'@w(e) is maximized. The Minimum Subgraph of Minimum Degree>=d (MSMD"d) problem involves finding a smallest subgraph of G with minimum degree at least d. Finally, the Dual Degree-densek-Subgraph (DDDkS) problem consists in finding a subgraph H of G such that |V(H)|@?k and the minimum degree in H is maximized.

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Index Terms

On the approximability of some degree-constrained subgraph problems
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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Copyright © Elsevier B.V. © 2012.

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Elsevier Science Publishers B. V.

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Published: 01 August 2012

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