The subject of this paper is the Independent Set problem for bounded node degree graphs. It is shown that the problem remains MAX SNP-complete even when graphs are restricted to being of degree bounded by 3 or to being 3-regular. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. We next study a better polynomial time approximation of the problem for degree 3 graphs. The performance ratio is improved from the previous best of 5/4 to arbitrarily close to 6/5 for degree 3 graphs and to 7/6 for cubic graphs. When combined with existing techniques this result also leads to approximation ratios, (B + 3)/5 + ε for the independent set problem and 2 - 5/(B + 3) + ε for the vertex cover problem on graphs of degree B, improving previous bounds for relatively small odd B.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computational Theory and Mathematics