Vilar, Julio Minimal cuts up to third order in a planar graph. (English) Zbl 0556.90025 IEEE Trans. Reliab. 33, 250-256 (1984). In the reliability evaluation of power distribution networks a subproblem is the determination of all the minimal cuts which isolate the substations from some load point. This problem can be modeled to determine all minimal cuts up to third order that isolate some sink node from all source nodes in a planar graph. This paper presents a new algorithm to obtain all the minimal cuts related to each sink node. The algorithm has the advantage of having a linear complexity. Reviewer: Ma Zhongfan (Beijing) MSC: 90B25 Reliability, availability, maintenance, inspection in operations research 90C90 Applications of mathematical programming 68Q25 Analysis of algorithms and problem complexity Keywords:reliability evaluation; power distribution networks; minimal cuts; planar graph; algorithm; linear complexity PDFBibTeX XMLCite \textit{J. Vilar}, IEEE Trans. Reliab. 33, 250--256 (1984; Zbl 0556.90025) Full Text: DOI