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Wappler, Markus : k-best solutions under Distance Constraints in Graphs

Wappler, Markus : k-best solutions under Distance Constraints in Graphs

Author(s):
Wappler, Markus
Title:
k-best solutions under Distance Constraints in Graphs
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 8, 2002
Mathematics Subject Classification:
05B35 [ Matroids, geometric lattices ]
05C12 [ Distance in graphs ]
52C45 [ Combinatorial complexity of geometric structures ]
90B40 [ Search theory ]
90B50 [ Management decision making, including multiple objectives ]
Abstract:
Based on former papers about valuated (Delta-)matroids we introduce the concept of a valuation of a graph. It is proved that in valuated Hamming graphs, a best solution as well as a 2-best solution with a given distance to the best solution can be reached via local research on shortest paths. Valuations of cubes are classified.
Keywords:
Combinatorial optimization, distance constraints, valuated (Delta-)matroids, Hamming graphs, cubes, convexity in graphs, local search, concave functions
Language:
German
Publication time:
8 / 2002