JUCS - Journal of Universal Computer Science 16(5): 715-728, doi: 10.3217/jucs-016-05-0715
On the Linear Number of Matching Substrings
expand article infoYo-Sub Han
‡ Yonsei University, Seoul, Republic of Korea
Open Access
We study the number of matching substrings in the pattern matching problem. In general, there can be a quadratic number of matching substrings in the size of a given text. The linearizing restriction enables to find at most a linear number of matching substrings. We first explore two well-known linearizing restriction rules, the longest-match rule and the shortest-match substring search rule, and show that both rules give the same result when a pattern is an infix-free set even though they have different semantics. Then, we introduce a new linearizing restriction, the leftmost nonoverlapping match rule that is suitable for find-and-replace operations in text searching, and propose an efficient algorithm for the new rule when a pattern is described by a regular expression. We also examine the problem of obtaining the maximal number of non-overlapping matching substrings.
string pattern matching, regular expression searching, linearizing restriction, Thompson automata