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Approximation Ratio of the Min-Degree Greedy Algorithm for Maximum Independent Set on Interval and Chordal Graphs (2403.10868v1)
Published 16 Mar 2024 in cs.DS
Abstract: In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval graphs of maximum degree 3. We show that on chordal graphs, the greedy algorithm is a $(1/2)$-approximation and that this is again tight. These results contrast with the known (tight) approximation ratio of $\frac{3}{\Delta+2}$ of the greedy algorithm for general graphs of maximum degree $\Delta$.
- It is hard to know when greedy is good for finding independent sets. Information Processing Letters, 61(2):101–106, 1997.
- Simple and local independent set approximation. Theoretical Computer Science, 846:27–37, 2020.
- R. Diestel. Graph Theory. Springer-Verlag Berlin and Heidelberg GmbH & Company KG, fifth edition, 2017.
- On the parameterized complexity of multiple-interval graph problems. Theoretical Computer Science, 410(1):53–61, 2009.
- M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979.
- M. Golumbic. Interval graphs and related topics. Discrete Mathematics, 55(2):113–121, 1985.
- MÂ Golumbic. Algorithmic Graph Theory and Perfect Graphs. ISSN. Elsevier, 2004.
- M. Halldórsson and J. Radhakrishnan. Greed is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica, 18(1):145–163, 1997.
- M. Halldórsson and K. Yoshihara. Greedy approximations of independent sets in low degree graphs. In John Staples, Peter Eades, Naoki Katoh, and Alistair Moffat, editors, Algorithms and Computation, 6th International Symposium, ISAAC ’95, Cairns, Australia, December 4-6, 1995, Proceedings, volume 1004 of LNCS, pages 152–161. Springer, 1995.
- Approximation algorithms for the weighted independent set problem in sparse graphs. Discrete Applied Mathematics, 157(4):617–626, 2009.
- Interval scheduling: A survey. Naval Research Logistics, 54(5):530–543, 2007.
- B. Korte and D. Hausmann. An analysis of the greedy heuristic for independence systems. In Annals of Discrete Mathematics, volume 2, pages 65–74. Elsevier, 1978.
- Ultimate greedy approximation of independent sets in subcubic graphs. In Shuchi Chawla, editor, Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 1436–1455. SIAM, 2020.
- The leafage of a chordal graph. Discussiones Mathematicae Graph Theory, 18(1):23–48, 1998.
- J. Mestre. Greedy in approximation algorithms. In Y. Azar and T. Erlebach, editors, Algorithms - ESA 2006, 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006, Proceedings, volume 4168 of LNCS, pages 528–539. Springer, 2006.
- C. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. Journal of Computer and System Sciences, 43(3):425–440, 1991.
- Algorithmic aspects of vertex elimination on graphs. SIAM Journal of Computing, 5(2):266–283, 1976.
- A note on greedy algorithms for the maximum weighted independent set problem. Discrete Applied Mathematics, 126(2-3):313–322, 2003.
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