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Related Experiment Video

Updated: May 9, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Parameterized Complexity and Inapproximability of Dominating Set Problem in Chordal and Near Chordal Graphs.

Chunmei Liu1, Yinglei Song

  • 1Dept. of Systems and Computer Science, Howard University, Washington, DC 20059, USA chunmei@scs.howard.edu.

Journal of Combinatorial Optimization
|July 23, 2013
PubMed
Summary

This study reveals the Dominating Set problem is W[2]-hard on chordal graphs, meaning it

Keywords:
Chordal graphsDominating setIndependent dominating setParameterized complexity

Related Experiment Videos

Last Updated: May 9, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Area of Science:

  • Graph Theory
  • Computational Complexity
  • Algorithm Analysis

Background:

  • The Dominating Set problem is a fundamental problem in graph theory.
  • Understanding its complexity on restricted graph classes is crucial for algorithm design.
  • Chordal and near chordal graphs are important graph classes with various applications.

Purpose of the Study:

  • To analyze the parameterized complexity of the Dominating Set problem on chordal and near chordal graphs.
  • To establish inapproximability results for computing minimum dominating sets in these graph classes.
  • To extend these findings to related problems like Independent Dominating Set and Connected Dominating Set.

Main Methods:

  • Parameterized complexity analysis using W-hierarchy.
  • Inapproximability proofs based on reductions.
  • Extension of techniques to related graph problems.

Main Results:

  • The Dominating Set problem is W[2]-hard on chordal and s-chordal (s > 3) graphs.
  • A polynomial-time 2-approximation algorithm for minimum dominating set in chordal graphs is not possible unless NP=P.
  • The approximation ratio for chordal graphs is improved by at most a factor of 3 compared to general graphs.

Conclusions:

  • The Dominating Set problem remains computationally challenging even on restricted graph classes like chordal graphs.
  • Significant improvements in approximation ratios are unlikely for minimum dominating sets in these graphs.
  • The techniques used provide insights into the complexity of related dominating set problems.