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Generalized Steiner problems and other variants. (English) Zbl 0980.90074

From the authors’ abstract: In this paper, combinatorial optimization problems are examined by considering the case that the ground set \(N\) is expressed as a union of \(m\) nonempty and distinct subsets \(N_1,\dots, N_m\). Motivated by the generalized traveling salesman problem the term used is that of generalized Steiner problems. A short list of classical combinatorial optimization problems is presented each member of which is adapted to the broader framework in order to identify possible links between these “generalized” problems. Well known from literature are Generalized Minimum Spanning Tree problems (GMST), the Generalized Traveling Salesman Problem (GTSP) and Subset Bin-Packing (SBP). Casting these problems into the new problem setting has important implications in terms of the time effort required to compute an optimal solution or a “good” solution to a problem. The authors examine questions like “Is the GTSP ‘harder’ than the TSP?” for a number of paradigmatic problems starting with ‘easy’ problems such as minimum spanning tree, assignment, Chinese postman or two-machine flow shop problems, and followed by ‘hard’ problems such as bin-packing and the TSP.

MSC:

90C27 Combinatorial optimization
90C60 Abstract computational complexity for mathematical programming problems
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