Polynomial Time Approximation Schemes for Some Dense Instances of NP-Hard Optimization Problems

We survey recent results on the existence of polynomial time approximation schemes for some dense instances of NP-hard combinatorial optimization problems. We indicate some inherent limits for the existence of such schemes for some other dense instances of optimization problems. We also go beyond the dense optimization problems and show how other approximation problems can be solved by using dense techniques. Received October 30, 1997; revised June 25, 1999, and April 17, 2000.