eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-07-02
71:1
71:19
10.4230/LIPIcs.ICALP.2021.71
article
LF Successor: Compact Space Indexing for Order-Isomorphic Pattern Matching
Ganguly, Arnab
1
Patel, Dhrumil
2
Shah, Rahul
2
Thankachan, Sharma V.
3
Department of Computer Science, University of Wisconsin - Whitewater, WI, USA
School of EECS, Louisiana State University, Baton Rouge, LA, USA
Department of Computer Science, University of Central Florida, Orlando, FL, USA
Two strings are order isomorphic iff the relative ordering of their characters is the same at all positions. For a given text T[1,n] over an ordered alphabet of size σ, we can maintain an order-isomorphic suffix tree/array in O(nlog n) bits and support (order-isomorphic) pattern/substring matching queries efficiently. It is interesting to know if we can encode these structures in space close to the text’s size of nlogσ bits. We answer this question positively by presenting an O(nlog σ)-bit index that allows access to any entry in order-isomorphic suffix array (and its inverse array) in t_{SA} = {O}(log²n/logσ) time. For any pattern P given as a query, this index can count the number of substrings of T that are order-isomorphic to P (denoted by occ) in {O}((|P|logσ+t_{SA})log n) time using standard techniques. Also, it can report the locations of those substrings in additional O(occ ⋅ t_{SA}) time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol198-icalp2021/LIPIcs.ICALP.2021.71/LIPIcs.ICALP.2021.71.pdf
Succinct data structures
Pattern Matching