Universal Succinct Representations of Trees?

Abstract. We consider the succinct representation of ordinal and cardinal trees on the RAM with logarithmic word size. Given a tree T, our representations support the following operations in O(1) time: (i) BP-substring(i, b), which reports the substring of length b bits (b is at most the wordsize) beginning at position i of the balanced parenthesis representation of T, (ii) DFUDS-substring(i, b), which does the same for the depth first unary degree sequence representation, and (iii) a similar operation for tree-partition based representations of T. We give: ? an asymptotically space-optimal 2n + o(n) bit representation of nnode ordinal trees that supports all the above operations with b = (log n), answering an open question from [He et al., ICALP'07]. ? an asymptotically space-optimal C(n, k)+o(n)-bit representation of k-ary cardinal trees, that supports (with b = ( log n)) the operations (ii) and (iii) above, on the ordinal tree obtained by removing labels from the cardinal tree...

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Arash Farzan, Rajeev Raman, S. Srinivasa Rao
• Keywords: Cardinal Tree Representation, ICALP 2009, Nnode Ordinal Trees, Ordinal Tree Operations, Theoretical Computer Science