Fast and Simple Jumbled Indexing for Binary RLE Strings

Important papers have appeared recently on the problem of indexing binary strings for jumbled pattern matching, and further lowering the time bounds in terms of the input size would now be a breakthrough with broad implications. We can still make progress on the problem, however, by considering other natural parameters. Badkobeh et al. (IPL, 2013) and Amir et al. (TCS, 2016) gave algorithms that index a binary string in O(n + ρ2 log ρ) time, where n is the length and ρ is the number of runs (i.e., maximal unary substrings). In this paper we first propose an algorithm which runs in O(n + ρ2) time and O(min{ρ2, n}) words of workspace. We then show how we can either keep the same bounds and store information that lets our index return the position of one match, or keep the same time bound and use only O(n) bits of workspace. 1998 ACM Subject Classification F.2.2 Combinatorial algorithms