Searching a bitstream in linear time for the longest substring of any given density

Details Searching a bitstream in linear time for the longest substring of any given density Searching a bitstream in linear time for the longest substring of any given density

2009-10-19

arxiv.org/abs/0910.3503v2

Algorithmica 61 (2011), no. 3, 555-579

Computer Science

Data Structures and Algorithms

22 pages, 19 figures; v2: minor edits and enhancements

Scientific paper

10.1007/s00453-010-9424-y

Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) reformulating the problem as a constrained walk through a sparse matrix, and then (ii) developing a data structure for this sparse matrix that allows us to perform each step of the walk in amortised constant time. We also give a linear time algorithm to find the longest substring whose ratio of ones to zeroes is bounded below by a given value. Both problems have practical relevance to cryptography and bioinformatics.

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