TY - GEN

T1 - Testing square-freeness of strings compressed by balanced straight line program

AU - Matsubara, Wataru

AU - Inenaga, Shunsuke

AU - Shinohara, Ayumi

PY - 2009/12/1

Y1 - 2009/12/1

N2 - In this paper we study the problem of deciding whether a given compressed string contains a square. A string x is called a square if x = zz and z = u k implies k = 1 and u = z. A string w is said to be square-free if no substrings of w are squares. Many efficient algorithms to test if a given string is square-free, have been developed so far. However, very little is known for testing square-freeness of a given compressed string. In this paper, we give an O(max(n 2, n log 2 N))-time O(n 2)-space solution to test square-freeness of a given compressed string, where n and N are the size of a given compressed string and the corresponding decompressed string, respectively. Our input strings are compressed by balanced straight line program (BSLP). We remark that BSLP has exponential compression, that is, N = O(2 n). Hence no decompress-then-test approaches can be better than our method in the worst case.

AB - In this paper we study the problem of deciding whether a given compressed string contains a square. A string x is called a square if x = zz and z = u k implies k = 1 and u = z. A string w is said to be square-free if no substrings of w are squares. Many efficient algorithms to test if a given string is square-free, have been developed so far. However, very little is known for testing square-freeness of a given compressed string. In this paper, we give an O(max(n 2, n log 2 N))-time O(n 2)-space solution to test square-freeness of a given compressed string, where n and N are the size of a given compressed string and the corresponding decompressed string, respectively. Our input strings are compressed by balanced straight line program (BSLP). We remark that BSLP has exponential compression, that is, N = O(2 n). Hence no decompress-then-test approaches can be better than our method in the worst case.

KW - Balanced straight line program

KW - Repetitions

KW - Squares

KW - String algorithm

KW - Text compression

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M3 - Conference contribution

AN - SCOPUS:84859645349

SN - 9781920682750

T3 - Conferences in Research and Practice in Information Technology Series

BT - Theory of Computing 2009 - Proceedings of the Fifteenth Computing

T2 - Theory of Computing 2009 - 15th Computing: The Australasian Theory Symposium, CATS 2009

Y2 - 20 January 2009 through 23 January 2009

ER -