Showing papers by "Daniel S. Hirschberg published in 1974"

Bounds on the Complexity of the Longest Common Subsequence Problem (Extended Abstract)

Abstract: [1] mentions the problem of finding long­ est common subsequences in less time than the product of the length of the strings involved. We say string x is a subsequence of string y if x can be formed by deleting some (not necessarily adjacent) symbols of y. x is a longest common subsequence (LCS) of Yl and Y2 if it is a subsequence of both Yl and Y2 and is as long as any other such string. Since the problem appears very hard, we believe that an attempt at a lower bound is in order. For a model, we treat algorithms as decision trees wi th "equal-not-equal" comparisons. The com­ plexity of an algorithm is the depth of the longest path in the tree. This model fits various algorithms that have appeared in the literature [2, 3, 4] and has been used to study the related string-to-string correction prob­ lem [5]. It does not apply to the recently discovered n2/10gn algorithm of Paterson [6] . Our goal is to show that no algorithm for the LCS problem modeled by these decision trees exists unless it is quadratic or assumes a fixed number of symbols in the alphabet.