Abstract
We present parallel approximation schemes for a large class of problems in logic and graph theory, when these problems are restricted to planar graphs and δ-near-planar graphs. Our results are based on the positive use of L-reductions, and the decomposition of a given graph into subgraphs for which the given problem can be solved optimally in polynomial time. The problems considered include MAX 3SAT, MAX SAT(S), maximum independent set, and minimum dominating set. Our NC-approximation schemes exhibit the same time versus performance tradeoff as those of Baker [Ba83]. For δ-near-planar graphs, this is the first time that approximation schemes of any kind have been obtained for these problems.
Supported by NSF Grants OCR 89-03319 and OCR 90-06396.
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Hunt, H.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E. (1994). Approximation schemes using L-reductions. In: Thiagarajan, P.S. (eds) Foundation of Software Technology and Theoretical Computer Science. FSTTCS 1994. Lecture Notes in Computer Science, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58715-2_136
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