New application of failure functions

Several algorithms are presented whose operations are governed by a principle of failure functions: when searching for an extremal value within a sequence, it suffices to consider only the subsequence of items each of which is the first possible improvement of its predecessor. These algorithms are more efficient than their more traditional counterparts

A sheaf-theoretic approach to pattern matching and related problems

AbstractWe present a general theory of pattern matching by adopting an extensional, geometric view of patterns. Representing the geometry of the pattern via a Grothendieck topology, the extension of the matching relation for a constant target and varying pattern forms a sheaf. We derive a generalized version of the Knuth-Morris-Pratt string-matching algorithm by gradually converting this extensional description into an intensional description, i.e., an algorithm. The generality of this approach is illustrated by briefly considering other applications: Earley's algorithm for parsing, Waltz filtering for scene analysis, matching modulo commutativity, and the n-queens problem

New Applications of Failure Functions

Several algorithms are presented whose operations are governed by a principle of failure functions: when searching for an extremal value within a sequence, it suffices to consider only the subsequence of items each of which is the first possible improvement of its predecessor. These algorithms are more efficient than their more traditional counterparts