Integer and combinatorial optimization
Integer and combinatorial optimization
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
On the consecutive ones property
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Introduction to Algorithms
Combination can be hard: approximability of the unique coverage problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Exact algorithms and applications for Tree-like Weighted Set Cover
Journal of Discrete Algorithms
Interference in cellular networks: the minimum membership set cover problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Set covering with almost consecutive ones property
Discrete Optimization
Parameterized Complexity
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The Minimum Membership Set Cover problem has recently been introduced and studied in the context of interference reduction in cellular networks. It has been proven to be notoriously hard in several aspects. Here, we investigate how natural generalizations and variations of this problem behave in terms of the consecutive ones property: While it is well-known that classical set covering problems become polynomial-time solvable when restricted to instances obeying the consecutive ones property, we experience a significantly more intricate complexity behavior in the case of Minimum Membership Set Cover. We provide polynomial-time solvability, NP-completeness, and approximability results for various cases here. In addition, a number of interesting challenges for future research is exhibited