Introduction to Domination Analysis

In the recently published book on the Traveling Salesman Problem, half of Chapter 6 [18] is devoted to domination analysis (DA) of heuristics for the Traveling Salesman Problem. Another chapter [16] is a detailed overview of the whole area of DA. Both chapters are of considerable length. The purpose of this paper is to give a short introduction to results and applications of DA. While we do not prove any significant new results, we provide proofs to a few extensions and improvements of previously known theorems. Some open problems are also raised. In Section 2 we provide motivation for studying DA. Basic terminology and notation are given in Section 3. The minimum multiprocessor scheduling problem is considered in some detail in Section 4. Section 5 overviews several results on other combinatorial optimization problems. Sections 6 and 7 are devoted to results on DA for the greedy algorithm and upper bounds on the maximum domination number for polynomial time traveling salesman heuristics.