TY - GEN

T1 - Alphabet independent two dimensional matching

AU - Amir, Amihood

AU - Benson, Gary

AU - Farach, Martin

N1 - Publisher Copyright:
© 1992 ACM.

PY - 1992/7/1

Y1 - 1992/7/1

N2 - There are many solutions to the string matching problem which are strictly linear in the input size and independent of alphabet size. Furthermore, the model of computation for these algorithms is very weak: they allow only simple arithmetic and comparisons of equality between characters of the input. In contrast, algorithm for two dimensional matching have needed stronger models of computation, most notably assuming a totally ordered alphabet. The fastest algorithms for two dimensional matching have therefore had a logarithmic dependence on the alphabet size. In the worst case, this gives an algorithm that runs in O(n2 log m) with O(m2 log m) preprocessing. We show an algorithm for two dimensional matching with an O(n2) text scanning phase. Furthermore, the text scan requires no special assumptions about the alphabet, i.e. it runs on the same model as the standard linear time string matching algorithm.

AB - There are many solutions to the string matching problem which are strictly linear in the input size and independent of alphabet size. Furthermore, the model of computation for these algorithms is very weak: they allow only simple arithmetic and comparisons of equality between characters of the input. In contrast, algorithm for two dimensional matching have needed stronger models of computation, most notably assuming a totally ordered alphabet. The fastest algorithms for two dimensional matching have therefore had a logarithmic dependence on the alphabet size. In the worst case, this gives an algorithm that runs in O(n2 log m) with O(m2 log m) preprocessing. We show an algorithm for two dimensional matching with an O(n2) text scanning phase. Furthermore, the text scan requires no special assumptions about the alphabet, i.e. it runs on the same model as the standard linear time string matching algorithm.

UR - http://www.scopus.com/inward/record.url?scp=0026992709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026992709&partnerID=8YFLogxK

U2 - 10.1145/129712.129719

DO - 10.1145/129712.129719

M3 - Conference contribution

AN - SCOPUS:0026992709

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 59

EP - 68

BT - Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992

PB - Association for Computing Machinery

T2 - 24th Annual ACM Symposium on Theory of Computing, STOC 1992

Y2 - 4 May 1992 through 6 May 1992

ER -