Sufficient conditions for the optimality of the greedy algorithm in greedoids

Abstract Greedy algorithms are among the most elementary ones in theoretical computer science and understanding conditions under which they yield an optimum solution is a widely studied problem. Greedoids were introduced by Korte Lovász at beginning of 1980s as generalization matroids. One basic motivations notion was to extend background behind greedy beyond well-known results on Indeed, many nature that cannot be interpreted matroid-theoretical context special cases algorithm greedoids. Although this turns out optimal surprisingly cases, no general theorem known explains phenomenon all these cases. Furthermore, certain claims regarding question made original works turned false only recently. The aim paper revisit straighten question: we summarize recent progress also prove new field. In particular, generalize result thus obtain sufficient condition for optimality covers much wider range applications than one.