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A Simple Optimal Representation for Balanced Parentheses

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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...
Richard F. Geary, Naila Rahman, Rajeev Raman, Venk
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where CPM
Authors Richard F. Geary, Naila Rahman, Rajeev Raman, Venkatesh Raman
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