Abstract
This chapter is devoted to some algorithm design techniques which became known by the term heuristics. The term heuristic in the area of combinatorial optimization is not unambiguously specified and so it is used with different meanings. A heuristic algorithm in a very general sense is a consistent algorithm for an optimization problem that is based on some transparent (usually simple) strategy (idea) of searching in the set of all feasible solutions, and that does not guarantee finding any optimal solution. In this context people speak about local search heuristics, or a greedy heuristic, even when this heuristic technique results in an approximation algorithm. In a narrow sense a heuristic is a technique providing a consistent algorithm for which nobody is able to prove that it provides feasible solutions of a reasonable quality in a reasonable (for instance, polynomial) time, but the idea of the heuristic seems to promise good behavior for typical instances of the optimization problem considered. Thus, a polynomial-time approximation algorithm cannot be considered as a heuristic in this sense, independently of the simplicity of its design idea. Observe that the description of a heuristic in this narrow sense is a relative term because an algorithm can be considered to be a heuristic one while nobody is able to analyze its behavior. But after proving some reasonable bounds on its complexity and the quality of the produced solutions (even with an error-bounded probability in the randomized case), this algorithm becomes a (randomized) approximation algorithm and is not considered to be a heuristic any more.
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Hromkovič, J. (2001). Heuristics. In: Algorithmics for Hard Problems. Texts in Theoretical Computer Science An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04616-6_6
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