Abstract
We investigate the power of a family of greedy algorithms for the independent set problem graphs of maximum degree three. These algorithm iteratively select vertices of minimum degree, but differ in the secondary rule for choosing among many candidates. We present two such algorithms that run in linear time, and show their performance ratios to be 3/2 and 9/7 ≈ 1.28, respectively. This also translates to good ratios for other classes of low-degree graphs.
We also show certain inherent limitations in the power of this family of algorithm: any algorithm that greedily selects vertices of minimum degree has a performance ratio at least 1.25 on degree-three graphs, even if given an oracle to choose among candidate vertices of minimum degree.
Research partly performed at Japan Advanced Institute of Science and Technology, IBM Tokyo Research Lab, and Max Planck Institut fuer Informatik.
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© 1995 Springer-Verlag Berlin Heidelberg
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Halldórsson, M.M., Yoshihara, K. (1995). Greedy approximations of independent sets in low degree graphs. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds) Algorithms and Computations. ISAAC 1995. Lecture Notes in Computer Science, vol 1004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015418
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DOI: https://doi.org/10.1007/BFb0015418
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