A Simple Optimal Representation for Balanced Parentheses

We consider succinct, or highly space-efficient, representations of a (static) string consisting of n pairs of balanced parentheses, that support natural operations such as finding the matching parenthesis for a given parenthesis, or finding the pair of parentheses that most tightly enclose a given pair. This problem was considered by Jacobson, [Proc. 30th FOCS, 549–554, 1989] and Munro and Raman, [SIAM J. Comput. 31 (2001), 762–776], who gave O(n)-bit and 2n + o(n)-bit representations, respectively, that supported the above operations in O(1) time on the RAM model of computation. This data structure is a fundamental tool in succinct representations, and has applications in representing suffix trees, ordinal trees, planar graphs and permutations. We consider the practical performance of parenthesis representations. First, we give a new 2n + o(n)-bit representation that supports all the above operations in O(1) time. This representation is conceptually simpler, its space bound ha...

• Type: Conference
• Year: 2004
• Where: CPM
• Authors: Richard F. Geary, Naila Rahman, Rajeev Raman, Venkatesh Raman
• Keywords: CPM 2004, Data Structures, Practical Performance, Succinct Representations