On Matroids with Multiple Objectives
- In this paper we investigate two optimization problems for matroids with multiple objective functions, namely finding the pareto set and the max-ordering problem which conists in finding a basis such that the largest objective value is minimal. We prove that the decision versions of both problems are NP-complete. A solution procedure for the max-ordering problem is presented and a result on the relation of the solution sets of the two problems is given. The main results are a characterization of pareto bases by a basis exchange property and finally a connectivity result for proper pareto solutions.
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| Author: | Matthias Ehrgott |
|---|---|
| URN: | urn:nbn:de:hbz:386-kluedo-48507 |
| Series (Serial Number): | Preprints (rote Reihe) des Fachbereich Mathematik (267) |
| Document Type: | Report |
| Language of publication: | English |
| Date of Publication (online): | 2017/10/16 |
| Year of first Publication: | 1995 |
| Publishing Institution: | Technische Universität Kaiserslautern |
| Date of the Publication (Server): | 2017/10/16 |
| Page Number: | 19 |
| Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
| DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
| Licence (German): |  Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0) |