Communications of the ACM - Special issue on parallelism
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Dynamic ordered sets with exponential search trees
Journal of the ACM (JACM)
Scaled and permuted string matching
Information Processing Letters
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
Sub-quadratic time and linear space data structures for permutation matching in binary strings
Journal of Discrete Algorithms
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Algorithms for computing Abelian periods of words
Discrete Applied Mathematics
| Hi-index | 0.89 |
Given a pattern P and a text T, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of P occurs in T. The indexed version of this problem, i.e., preprocessing a string to efficiently answer such permutation queries, is hard and has been studied in the last few years. Currently the best bounds for this problem are O(n^2/log^2n) (with O(n) space and O(1) query time) (Moosa and Rahman (2012) [1]) and O(r^2logr) (with O(|L|) space and O(log|L|) query time) (Badkobeh et al. (2012) [2]), where r is the length of the run-length encoding of T and |L|=O(n) is the size of the index. In this paper we present new results for this problem. Our first result is an alternative construction of the index by Badkobeh et al. (2012) [2] that obtains a trade-off between the space and the time complexity. It has O(r^2logk+n/k) complexity to build the index, O(logk) query time, and uses O(n/k+|L|) space, where k is a parameter. The second result is an O(n^2log^2w/w) algorithm (with O(n) space and O(1) query time), based on word-level parallelism where w is the word size in bits.