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- W89478800 abstract "In this paper we consider linear programs with a 0–1 constraint matrix A, arbitrary integral right hand sides b and objective functions determined jointly by an arbitrary nonnegative vector d and the constraint matrix itself (in three different ways). Absence of a particular minor of A is shown to be a necessary condition for the existence of an integral optimal solution for all integral b and all objective functions generated as stated above. If A is the incidence matrix of arcs vs. s-t paths of an undirected graph, then the absence of this minor is also sufficient for integrality. In graph theoretic terms, this condition is the same as the graph being series-parallel. Efficient algorithms and examples are provided for each of the problems in this case.Key wordsLinear ProgramTotal Dual IntegralitySeries Parallel Graphs" @default.
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- W89478800 date "1985-01-01" @default.
- W89478800 modified "2023-09-27" @default.
- W89478800 title "Classes of linear programs with integral optimal solutions" @default.
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- W89478800 doi "https://doi.org/10.1007/bfb0121053" @default.
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