Greedy Algorithms in Combinatorial Optimization

Abstract

The greedy algorithm is perhaps the intuitively most natural optimization principle: take in each step the locally best decision, where “best” is measured by an objective function that is evaluated locally. The question, then, arises under what conditions such a local strategy leads to a globally optimal solution. Particular attention has therefore been payed to combinatorial structures for which the greedy algorithm works provably optimally (at least relative to certain types of objective functions): for example, matroids, polymatroids and their generalizations (e.g., greedoids).