Given an undirected graph, we study the capacitated vertex separator problem
that asks to find a subset of vertices of minimum cardinality, the removal of which induces a
graph having a bounded number of pairwise disconnected shores (subsets of vertices) of
limited cardinality. The problem is of great importance in the analysis and protection of communication or social networks against possible viral attacks and for matrix decomposition algorithms. In this article, we provide a new bilevel interpretation of the problem and model it
as a two-player Stackelberg game in which the leader interdicts the vertices (i.e., decides on
the subset of vertices to remove), and the follower solves a combinatorial optimization problem on the resulting graph. This approach allows us to develop a computational framework
based on an integer programming formulation in the natural space of the variables. Thanks
to this bilevel interpretation, we derive three different families of strengthening inequalities
and show that they can be separated in polynomial time. We also show how to extend these
results to a min-max version of the problem. Our extensive computational study conducted
on available benchmark instances from the literature reveals that our new exact method is
competitive against the state-of-the-art algorithms for the capacitated vertex separator problem and is able to improve the best-known results for several difficult classes of instances.
The ideas exploited in our framework can also be extended to other vertex/edge deletion/
insertion problems or graph partitioning problems by modeling them as two-player Stackel-
berg games and solving them through bilevel optimization.
Dettaglio pubblicazione
2022, OPERATIONS RESEARCH, Pages 2399-2420 (volume: 70)
Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem (01a Articolo in rivista)
Furini F., Ljubic I., Malaguti E., Paronuzzi P.
Gruppo di ricerca: Combinatorial Optimization
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