Greedy Like Algorithms for the Traveling Salesman and Multidimensional Assignment Problems

Majority of chapters of this book show usefulness of greedy like algorithms for solving various combinatorial optimization problems. The aim of this chapter is to warn the reader that not always a greedy like approach is a good option and, in certain cases, it is a very bad option being sometimes among the worst possible options. Our message is not a discouragement from using greedy like algorithms altogether; we think that for every combinatorial optimization problem of importance, researchers and practitioners should simply investigate the appropriateness of greedy like algorithms and the existence of better alternatives to them (considering both quality of solution and running time). In many cases, especially when the running time must be very short, the conclusion may still be that the most practical of known approaches is a greedy like algorithm.