Faster Compressed Dictionary Matching

Abstract

Given a set ${\cal D}$ of d patterns, the dictionary matching problem is to index ${\cal D}$ such that for any query text T, we can locate the occurrences of any pattern within T efficiently. When ${\cal D}$ contains a total of n characters drawn from an alphabet of size σ, Hon et al. (2008) gave an $nH_k({\cal D}) + o(n \log \sigma)$-bit index which supports a query in O(|T| (log^ε n + logd) + occ) time, where ε> 0 and $H_k({\cal D})$ denotes the kth order entropy of ${\cal D}$. Very recently, Belazzougui (2010) proposed an elegant scheme, which takes n logσ + O(n) bits of index space and supports a query in optimal O(|T| + occ) time. In this paper, we provide connections between Belazzougui’s index and the XBW compression of Ferragina et al. (2005), and show that Belazzougui’s index can be slightly modified to be stored in $nH_k({\cal D}) + O(n)$ bits, while query time remains optimal; this improves the compressed index by Hon et al. (2008) in both space and time.

This work is supported in part by Taiwan NSC Grant 96-2221-E-007-082 and US NSF Grants CCF-1017623 and CCF-0621457.