Band-Pivot Prim: Breaking the Sorting Barrier for Minimum Spanning Tree in the Comparison-Addition Model

Keywords: minimum spanning tree; sorting barrier; comparison-addition model

Abstract:

We present the \emph{Band--Pivot Prim} algorithm, a deterministic exact minimum spanning tree (MST) algorithm for weighted undirected graphs with arbitrary real weights in the comparison--addition model.
In analogy to recent $O(m\log^{2/3}n)$ single-source shortest path (SSSP) results, our approach removes the classic $\log n$ priority-queue factor in Prim's algorithm by avoiding the maintenance of a total order over the entire frontier.
We group candidate edges into \emph{bands} by weight, apply bounded expansions from a reduced \emph{pivot set}, and maintain only a partial order of keys exposed in small blocks.
For graphs of constant degree (or after degree reduction), this yields an $O(m\log^{2/3}n)$ deterministic algorithm in the comparison-addition model, improving over the standard $O(m + n\log n)$ bound for sparse graphs with arbitrary real weights.

Submission Number: 26