Abstract
This chapter deals with a special degeneracy problem, namely the problem of determining all neighbouring vertices of a degenerate vertex of a convex polytope. In the following we call it the neighbourhood problem. The determination of all neighbouring vertices of a nondegenerate vertex is unproblematic, since a nondegenerate vertex has exactly one pivot tableau and all neighbouring vertices can be determined on the basis of this tableau in one pivot step each time. In contrast to this, a degenerate vertex xo is associated with different pivot tableaux, and in exceptional cases only can all neighbouring vertices be computed using just one pivot tableau of xo 1).
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© 1986 Springer-Verlag Berlin Heidelberg
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Kruse, HJ. (1986). A Method to Solve the Neighbourhood Problem. In: Degeneracy Graphs and the Neighbourhood Problem. Lecture Notes in Economics and Mathematical Systems, vol 260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-49270-9_5
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DOI: https://doi.org/10.1007/978-3-642-49270-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16049-6
Online ISBN: 978-3-642-49270-9
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