Faster Regular Expression Matching

Regular expression matching is a key task (and often the computational bottleneck) in a variety of widely used software tools and applications, for instance, the unix grep and sed commands, scripting languages such as awk and perl, programs for analyzing massive data streams, etc. We show how to solve this ubiquitous task in linear space and O(nm(log log n)/(log n)+n+m) time where m is the length of the expression and n the length of the string. This is the first improvement for the dominant O(nm/ log n) term in Myers’ O(nm/ log n+(n+m) log n) bound [JACM 1992]. We also get improved bounds for external memory.