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arXiv · 2603.27530

A gentle tutorial on Bock's algorithm for minimum directed spanning trees with a structured reformulation

Yuxi Wang·Jungyeul Park
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Abstract

Bock's 1971 algorithm is an exact primal--dual method for the minimum-cost arborescence problem, but its Algol presentation obscures the interaction of its maintained arrays and label-directed control flow. We provide a self-contained tutorial comprising the original listing, a line-mapped explanation, a circuit-forming three-node example, and a complete trace of Bock's ten-node instance. We also present a structured reformulation that replaces temporary span-label changes with explicit component and trace state. Local tightness and contraction-progress results, together with an operational-correspondence theorem, establish that the reformulation preserves Bock's candidate choices, transfers, and final solution.

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Yuxi Wang, Jungyeul Park. 2026-03-29. A gentle tutorial on Bock's algorithm for minimum directed spanning trees with a structured reformulation. https://arxiv.org/abs/2603.27530

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