A UNIFIED APPROXIMATION ALGORITHM FOR NODE-DELETION PROBLEMS

In this paper we consider a unified (polynomial time) approximation me thod for node-deletion problems with nontrivial and hereditary graph p roperties. One generic algorithm scheme is presented, which can be app lied to any node-deletion problem for finding approximate solutions. I t will be shown then that the quality of solutions found by this algor ithm is determined by the quality of any minimal solution in any graph in which nodes are weighted according to a certain scheme chosen by t he algorithm. For various node-deletion problems simple and natural sc hemes 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. (C) 1998 Elsevier Science B.V. All rights res erved.