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.
| Author: | Bernhard MöllerGND, Peter Höfner |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-572621 |
| Frontdoor URL | https://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 |
| Type: | Report |
| Language: | English |
| Date of Publication (online): | 2019/06/28 |
| Year of first Publication: | 2019 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2019/06/28 |
| Page Number: | 10 |
| 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 |
