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Algebraic Algorithm Design and Local Search

机译：代数算法设计与局部搜索

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Formal, mathematically-based techniques promise to play an expanding role in thedevelopment and maintenance of the software on which our technological society depends. Algebraic techniques have been applied successfully to algorithm synthesis by the use of algorithm theories and design tactics, an approach pioneered in the Kestrel Interactive Development System (KIDS). An algorithm theory formally characterizes the essential components of a family of algorithms. A design tactic is a specialized procedure for recognizing in a problem specification the structures identified in an algorithm theory and then synthesizing a program. Design tactics are hard to write, however, and much of the knowledge they use is encoded procedurally in idiosyncratic ways. Algebraic methods promise a way to represent algorithm design knowledge declaratively and uniformly. We describe a general method for performing algorithm design that is more purely algebraic than that of KIDS. This method is then applied to local search. Local search is a large and diverse class of algorithms applicable to a wide range of problems; it is both intrinsically important and representative of algorithm design as a whole. A general theory of local search is formalized to describe the basic properties common to all local search algorithms, and applied to several variants of hill climbing and simulated annealing. The general theory is then specialized to describe some more advanced local search techniques, namely tabu search and the Kernighan-Lin heuristic.

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