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Journals ACM SIGACT News Volume 31 Issue 3

A Potential-Based Amortized Analysis of th e Union-Find Data Structur e Gregory C . Harfst* Edward M . Reingold f i August 3, 200 0 Abstract . We present a simple, new potential-based amortized analysis for the standar d union-find data structure . Key words . Amortized analysis, potential functions, disjoint sets, Tarjan's multiple partitioning, Ackermann's function AMS(MOS) subject classifications . 68P05, 68Q25, 68R9 9 The standard union-find data structure is simple to describe, yet has a complex analysis . Traditionally the amortized analysis of this structure is done using the accounting method . We present a simple, new potential-based analysis covering several of the most interestin g results . 1 Disjoint Set Data Structur e As usual, we implement the disjoint set data structure as a collection of trees (for a fulle r discussion see [1], [2], [3], or [4]) . The root of each tree is the canonical element for all th e nodes contained within its tree . The data structure supports the operations makeset(x) , link(x, y) and find(x) . The operation makeset(x) takes an element x and makes it a singleton node with parent(x) _ x . This makes x the canonical element

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A potential-based amortized analysis of the union-find data structure

Harfst, Gregory C.; Reingold, Edward M.
ACM SIGACT News , Volume 31 (3)
Association for Computing Machinery – Sep 1, 2000

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