TY  - RPRT
A1  - Möller, Bernhard
A1  - Höfner, Peter
T1  - A new correctness proof for prim's algorithm
N2  - 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.
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2019-02 
Y1  - 2019
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/57262
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-572621
PB  - Universität Augsburg
CY  - Augsburg
ER  -