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What about future? Robustness under vertex-uncertainty in graph-problems

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Date
2006
Publisher city
Paris
Collection title
Cahier du LAMSADE
Collection Id
236
Link to item file
https://hal.archives-ouvertes.fr/hal-00957556
Dewey
Recherche opérationnelle
Sujet
graph-problems
URI
https://basepub.dauphine.fr/handle/123456789/20907
Collections
  • LAMSADE : Publications
Metadata
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Author
Murat, Cécile
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Paschos, Vangelis
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Type
Document de travail / Working paper
Abstract (EN)
We study a robustness model for graph-problems under vertex-uncertainty. We assume that any vertex vi of the input-graph G(V,E) has only a probability pi to be present in the final graph to be optimized (i.e., the final instance for the problem tackled will be only a sub-graph of the initial graph). Under this model, the original "deterministic" problem gives rise to a new (deterministic) problem on the same input-graph G, having the same set of feasible solutions as the former one, but its objective function can be very different from the original one, the set of its optimal solutions too. Moreover, this objective function is a sum of 2 / v / terms; hence, its computation is not immediately polynomial. We give sufficient conditions for large classes of graph-problems under which objective functions of the robust counterparts are polynomially computable and optimal solutions are well-characterized. Finally, we apply these general results to natural and well-known representatives of any of the classes considered.

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