Tarjan: inverse-Ackermann analysis of weighted union and path compression

What changed

Tarjan established nearly linear amortized bounds for weighted union with path compression, with inverse-Ackermann dependence, and a matching lower-bound analysis within the studied tree-algorithm model.

Scientific scope

Tarjan established nearly linear amortized bounds for weighted union with path compression, with inverse-Ackermann dependence, and a matching lower-bound analysis within the studied tree-algorithm model. The amortized bound concerns the specified sequence of disjoint-set operations and union/path-compression rules in its computational model. It is not a worst-case constant bound for each operation or every variant. Input size, storage and operation accounting remain. Later refinements and implementations retain separate credit.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• Robert Endre Tarjan · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Tarjan — original Berkeley ERL-M 4341974 report
• Tarjan —1975 Journal of the ACM publisher deposit
• Galler/Fischer report citation —1964 publisher identity and date deposit

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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