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2 Fundamenta Informaticae

2 2018

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On Computing Average Common Substring Over Run Length Encoded Sequences

Hooshmand S., Abedin P., Tavakoli N., Thankachan S. V.

Fundamenta Informaticae

2018

Vol. 163, nr 3

267--273

The Average Common Substring (ACS) is a popular alignment-free distance measure for phylogeny reconstruction. The ACS of a sequence X[1; x] w.r.t. another sequence Y[1; y] is ACS(X;Y) =[formula] The lcp(., .) of two input sequences is the length of their longest common prefix. The ACS can be computed in O(n) space and time, where n = x + y is the input size. The compressed string matching is the study of string matching problems with the following twist: the input data is in a compressed format and the underling task must be performed with little or no decompression. In this paper, we revisit the ACS problem under this paradigm where the input sequences are given in their run-length encoded format. We present an algorithm to compute ACS(X,Y) in O(N log N) time using O(N) space, where N is the total length of sequences after run-length encoding.

A Linear Space Data Structure for Range LCP Queries

Ganguly A., Shah R., Patil M., Thankachan S. V.

Fundamenta Informaticae

2018

Vol. 163, nr 3

245--251

Range LCP (longest common prefix) is an extension of the classical LCP problem and is defined as follows: Preprocess a string S[1...n] of n characters, such that whenever an interval [i; j] comes as a query, we can report max{LCP(Sp,Sq) i ≤ p < q ≤ j} Here LCP((Sp, Sq) is the longest common prefix of the suffixes of S starting at locations p and q, and LCP((Sp,Sq)) is its length. This problem was first addressed by Amir et al. [ISAAC, 2011]. They showed that the query can be answered in O(log log n) time using an O(n log 1+ε n) space data structure for an arbitrarily small constant ε > 0. In an attempt to reduce the space bound, they presented a linear space data structure of O(d log log n) query time, where d = (j - i + 1). In this paper, we present a new linear space data structure with an improved query time of O[formula].