Theory of linear and integer programming
Theory of linear and integer programming
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Fast approximation algorithms for multicommodity flow problems
Selected papers of the 23rd annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
The complexity of restricted spanning tree problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
0/1-Integer Programming: Optimization and Augmentation are Equivalent
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Bicriteria Spanning Tree Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
The constrained minimum weighted sum of job completion times problem
Mathematical Programming: Series A and B
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
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We provide preliminary results regarding the existence of a polynomial time approximation scheme (PTAS) for minimizing a linear function over a 0/1 covering polytope which is integral, with one additional covering constraint. Our algorithm is based on extending the methods of Goemans and Ravi for the constrained minimum spanning tree problem and, in particular, implies the existence of a PTAS for several covering integer programming problems with a totally unimodular constraint matrix. These include the cases when the columns of the constraint matrix either: have at most two nonzero elements; are incidence vectors of a laminar family; or have consecutive ones and no column is contained in another.