Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
New indices for text: PAT Trees and PAT arrays
Information retrieval
Journal of the ACM (JACM)
SIAM Journal on Computing
Bonsai: a compact representation of trees
Software—Practice & Experience
Suffix arrays: a new method for on-line string searches
SIAM Journal on Computing
Surpassing the information theoretic bound with fusion trees
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Compact pat trees
Efficient suffix trees on secondary storage
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Membership in Constant Time and Almost-Minimum Space
SIAM Journal on Computing
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Succinct representation of balanced parentheses, static trees and planar graphs
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Succinct static data structures
Succinct static data structures
Space-efficient static trees and graphs
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Structuring labeled trees for optimal succinctness, and beyond
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Technical Section: A multimedia framework for effective language training
Computers and Graphics
NETWORKING'05 Proceedings of the 4th IFIP-TC6 international conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communication Systems
Succinct ordinal trees based on tree covering
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Hi-index | 0.00 |
This paper focuses on space efficient representations of trees that permit basic navigation in constant time. While most of the previous work has focused on binary trees, we turn our attention to trees of higher degree. We consider both cardinal trees (rooted trees where each node has k positions each of which may have a reference to a child) and ordinal trees (the children of each node are simply ordered). Our representations use a number of bits within a lower order term of the information theoretic lower bound. For cardinal trees the structure supports finding the parent, child i or subtree size of a given node. For ordinal trees we support the operations of finding the degree, parent, ith child and subtree size. These operations provide a mapping from the n nodes of the tree onto the integers [1, n] and all are performed in constant time, except finding child i in cardinal trees. For k-ary cardinal trees, this operation takes O(lg lg k) time for the worst relationship between k and n, and constant time if k is much less than n.