ACM Computing Surveys (CSUR)
Indexing permutations for binary strings
Information Processing Letters
On table arrangements, scrabble freaks, and jumbled pattern matching
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Sub-quadratic time and linear space data structures for permutation matching in binary strings
Journal of Discrete Algorithms
On Approximate Jumbled Pattern Matching in Strings
Theory of Computing Systems - Special Issue: Fun with Algorithms
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Algorithms for computing Abelian periods of words
Discrete Applied Mathematics
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The Binary Jumbled String Matching Problem is defined as follows: Given a string s over {a,b} of length n and a query (x,y), with x,y non-negative integers, decide whether s has a substring t with exactly x a@?s and y b@?s. Previous solutions created an index of size O(n) in a pre-processing step, which was then used to answer queries in constant time. The fastest algorithms for construction of this index have running time O(n^2/logn) (Burcsi et al., 2010 [1]; Moosa and Rahman, 2010 [7]), or O(n^2/log^2n) in the word-RAM model (Moosa and Rahman, 2012 [8]). We propose an index constructed directly from the run-length encoding of s. The construction time of our index is O(n+@r^2log@r), where O(n) is the time for computing the run-length encoding of s and @r is the length of this encoding-this is no worse than previous solutions if @r=O(n/logn) and better if @r=o(n/logn). Our index L can be queried in O(log@r) time. While |L|=O(min(n,@r^2)) in the worst case, preliminary investigations have indicated that |L| may often be close to @r. Furthermore, the algorithm for constructing the index is conceptually simple and easy to implement. In an attempt to shed light on the structure and size of our index, we characterize it in terms of the prefix normal forms of s introduced in Fici and Liptak (2011) [6].