Max Crochemore

Computing and Combinatorics: 23rd International Conference, COCOON 2017, Hong Kong, China, August 3-5, 2017, Proceedings

A word of the form WW for some word \(W\in \varSigma ^*\) is called a square, where \(\varSigma \) is an alphabet. A partial word is a word possibly containing holes (also called don’t cares). The hole is a special symbol Open image in new window which matches (agrees with) any symbol from Open image in new window . A p-square is a partial word matching at least one square WW without holes. Two p-squares are called equivalent if they match the same set of squares. We denote by \( psquares (T)\) the number of non-equivalent p-squares which are factors of a partial word T. Let \(\mathrm {PSQUARES}_k(n)\) be the maximum value of \( psquares (T)\) over all partial words of length n with at most k holes. We show asymptotically tight bounds:

LATIN 2016: Theoretical Informatics: 12th Latin American Symposium, Ensenada, Mexico, April 11-15, 2016, Proceedings

c_1\cdot \min (nk^2,\, n^2) \le \mathrm {PSQUARES}_k(n) \le c_2\cdot \min (nk^2,\, n^2)

6th international conference on music information retrieval

for some constants \(c_1,c_2>0\). We also present an algorithm that computes \( psquares (T)\) in \(\mathcal {O}(nk^3)\) time for a partial word T of length n with k holes. In particular, our algorithm runs in linear time for \(k=\mathcal {O}(1)\) and its time complexity near-matches the maximum number of non-equivalent p-square factors in a partial word.

Prague Stringology Conference 2008

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as q-gram distance, are usually computed in time linear with respect to the length of the sequences. In this article, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an absent word of some sequence if it does not occur in the sequence. An absent word is minimal if all its proper factors occur in the sequence. Here we present the first linear-time and linear-space algorithm to compare two sequences by considering all their minimal absent words. In the process, we present results of combinatorial interest, and also extend the proposed techniques to compare circular sequences.

Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free techniques, which are based on measures referring to the composition of sequences in terms of their constituent patterns. These measures, such as q-gram distance, are usually computed in time linear with respect to the length of the sequences. In this article, we focus on the complementary idea: how two sequences can be efficiently compared based on information that does not occur in the sequences. A word is an absent word of some sequence if it does not occur in the sequence. An absent word is minimal if all its proper factors occur in the sequence. Here we present the first linear-time and linear-space algorithm to compare two sequences by considering all their minimal absent words. In the process, we present results of combinatorial interest, and also extend the proposed techniques to compare circular sequences.