I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
I/O-efficient batched union-find and its applications to terrain analysis
ACM Transactions on Algorithms (TALG)
Applications of forbidden 0-1 matrices to search tree and path compression-based data structures
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Top-Down analysis of path compression: deriving the inverse-ackermann bound naturally (and easily)
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Union-find with constant time deletions
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We present a new analysis of the worst-case cost of path compression, which is an operation that is used in various well-known "union-find" algorithms. In contrast to previous analyses which are essentially based on bottom-up approaches, our method proceeds top-down, yielding recurrence relations from which the various bounds arise naturally. In particular the famous quasi-linear bound involving the inverse Ackermann function can be derived without having to introduce the Ackermann function itself.