A new correctness proof for prim's algorithm

  • We present a new correctness proof for Prim's algorithm. The standard proof establishes the invariant that each iteration constructs a subtree of some minimal spanning tree, and heavily relies on the existence of a spanning tree of the overall graph, as well as an `edge exchange' property, which includes reasoning about graph cycles. We establish a stronger property showing that the algorithm builds a minimal spanning tree in each step, w.r.t. the vertices already covered. As a consequence, the proof neither uses the existence of a minimal spanning tree of the entire graph, nor the classical exchange property.

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Author:Bernhard MöllerGND, Peter Höfner
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/57262
Series (Serial Number):Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg (2019-02)
Publisher:Universität Augsburg
Place of publication:Augsburg
Year of first Publication:2019
Publishing Institution:Universität Augsburg
Release Date:2019/06/28
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):Deutsches Urheberrecht mit Print on Demand