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

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.

Computation and Language (cs.CL)

arXiv:2603.27530 [cs.CL]

(or arXiv:2603.27530v2 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2603.27530 Focus to learn more arXiv-issued DOI via DataCite

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