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The dominating set problem is a core NP-hard problem in combinatorial optimization and graph theory, and has many important applications. Baker [JACM 41,1994] introduces a k-outer planar graph decomposition-based framework for designing polynomial time approximation scheme (PTAS) for a class of NP-hard problems in planar graphs. It is mentioned that the framework can be applied to obtain an O(2 ck n) time, c is a constant, (1 + 1/k)-approximation algorithm for the planar dominating set problem.doi:10.3390/a6010043 fatcat:u6dugxkniza25dqs56wejmwh6m