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CSR
2010
Springer

Validating the Knuth-Morris-Pratt Failure Function, Fast and Online

9 years 8 months ago
Validating the Knuth-Morris-Pratt Failure Function, Fast and Online
Let πw denote the failure function of the Knuth-Morris-Pratt algorithm for a word w. In this paper we study the following problem: given an integer array A [1 . . n], is there a word w over arbitrary alphabet Σ such that A [i] = πw[i] for all i? Moreover, what is the minimum cardinality of Σ required? We give an elementary and self-contained O(n log n) time algorithm for this problem, thus improving the previously known solution [6], which had no polynomial running time bound. Then, using both a deeper combinatorial insight into the structure of π and more advanced tools, we improve the running time to O(n).
Pawel Gawrychowski, Artur Jez, Lukasz Jez
Added 19 Jul 2010
Updated 19 Jul 2010
Type Conference
Year 2010
Where CSR
Authors Pawel Gawrychowski, Artur Jez, Lukasz Jez
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