Abstract
LetE be a finite set, ℱ be a family of subsets ofE and¯C be a capacity vector for all elements ofE. For eachF∈ℱ, define thecapacity ofF as the minimum capacity occurring inF. The problem which we discuss in this paper is how to change the vector¯C as little as possible so that a givenF 0∈8o has the maximum capacity. This model contains inverse maximum capacity spanning tree problem, inverse maximum capacity path problem and etc. as its special cases. We transform the problem into the minimum weight cut set problem and show that this problem can be solved efficiently if an efficient algorithm for finding minimum weight cut set of ℱ is available.
Zusammenfassung
Sei ℱ eine Familie von Teilmengen einer endlichen MengeE und¯C ein Kapazitätsvektor bzgl. der Elemente vonE. Für jedesF∈ℱ sei dieKapazität vonF als die minimale inF auftretende Kapazität definiert. Das in dieser Arbeit untersuchte Problem besteht darin, den Vektor¯C so wenig wie möglich abzuändern, sodass ein vorgegebenesF 0∈ℱ maximale Kapazität besitzt. Dieses Modell enthält die inversen Probleme maximaler Kapazität bei aufspannenden Bäumen, Pfaden usw. als Spezialfälle.
Wir transformieren das Problem in ein gewichtetes Schnittmengenproblem und zeigen, dass das Problem effizient lösbar ist, wenn ein effizienter Algorithmus zur Bestimmung einer minimalen Schnittmenge bzgl. ℱ zur Verfügung steht.
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The authors gratefully acknowledge the partial support of the Hong Kong Research Grant Council (CityU Grant # 9040189)
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Yang, C., Zhang, J. Inverse maximum capacity problems. OR Spektrum 20, 97–100 (1998). https://doi.org/10.1007/BF01539860
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DOI: https://doi.org/10.1007/BF01539860
Key words
- Inverse problems
- minimum weight cut set
- maximum capacity tree
- maximum capacity path
- minimum unrestricted cut