A unified approximation algorithm for node-deletion problems

• Published in: Discrete Applied Mathematics Vol. 86; no. 2; pp. 213 - 231
• Main Author: Fujito, Toshihiro
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.09.1998; Amsterdam Elsevier; New York, NY
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximation algorithm; Computer science; control theory; systems; Exact sciences and technology; Hereditary graph property; Information retrieval. Graph; Local ratio theorem; Node-deletion problem; Performance ratio; Theoretical computing; Node-deletion problem; Approximation algorithm; Local ratio theorem; Performance ratio; Hereditary graph property; Minimal graph; Graph node; Algorithm complexity; Optimization method; Approximation theory; Graph theory; Polynomial time
• ISSN: 0166-218X; 1872-6771
• DOI: 10.1016/S0166-218X(98)00035-3

In this paper we consider a unified (polynomial time) approximation method for node-deletion problems with nontrivial and hereditary graph properties. One generic algorithm scheme is presented, which can be applied to any node-deletion problem for finding approximate solutions. It will be shown then that the quality of solutions found by this algorithm is determined by the quality of any minimal solution in any graph in which nodes are weighted according to a certain scheme chosen by the algorithm. For various node-deletion problems simple and natural schemes for weight assignment are considered. It will be proven that the weight of any minimal solution is a good approximation to the optimal weight when graphs are weighted according to them, implying that our generic algorithm indeed computes good approximate solutions for those node-deletion problems.