Greedy and Heuristic Algorithms for Codes and Colorings

Many of the fundamental coding problems can be represented as graph problems. These problems are often intrinsically difficult and unsolved even if the code length is relatively small. With the motivation to improve lower bounds on the sizes of constant weight codes and asymmetric codes, we suggest a few greedy algorithms and other heuristic methods, which result in new, record-breaking codes. Some of the heuristics used are based on tabu search and evolutionary algorithms. Tables of new codes are presented.