On a class of interdiction problems with partition matroids: complexity and polynomial-time algorithms
CoRR(2024)
摘要
In this study, we consider a class of linear matroid interdiction problems,
where the feasible sets for the upper-level decision-maker (referred to as the
leader) and the lower-level decision-maker (referred to as the follower) are
given by partition matroids with a common ground set. In contrast to classical
network interdiction models where the leader is subject to a single budget
constraint, in our setting, both the leader and the follower are subject to
several independent cardinality constraints and engage in a zero-sum game.
While a single-level linear integer programming problem over a partition
matroid is known to be polynomially solvable, we prove that the considered
bilevel problem is NP-hard, even when the objective function coefficients are
all binary. On a positive note, it turns out that, if the number of cardinality
constraints is fixed for either the leader or the follower, then the considered
class of bilevel problems admits several polynomial-time solution schemes.
Specifically, these schemes are based on a single-level dual reformulation, a
dynamic programming-based approach, and a 2-flip local search algorithm for the
leader.
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