Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Rounding algorithms for covering problems
Mathematical Programming: Series A and B
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
An extension of the Lovász local lemma, and its applications to integer programming
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximating low-congestion routing and column-restricted packing problems
Information Processing Letters - Special issue analytical theory of fuzzy control with applications
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Approximation algorithms
Approximation Algorithms for Single-Source Unsplittable Flow
SIAM Journal on Computing
A Constant-Factor Approximation Algorithm for Packet Routing and Balancing Local vs. Global Criteria
SIAM Journal on Computing
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Tight Approximation Results for General Covering Integer Programs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximation algorithms for covering/packing integer programs
Journal of Computer and System Sciences
Exact Algorithms for Set Multicover and Multiset Multicover Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Dynamic programming based algorithms for set multicover and multiset multicover problems
Theoretical Computer Science
On capacitated set cover problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximation schemes for deal splitting and covering integer programs with multiplicity constraints
Theoretical Computer Science
Approximation schemes for deal splitting and covering integer programs with multiplicity constraints
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
On column-restricted and priority covering integer programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Set cover revisited: hypergraph cover with hard capacities
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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In a covering integer program (CIP), we seek an n-vector x of nonnegative integers, which minimizes cT ċ x, subject to Ax ≥ b, where all entries of A, b, c are nonnegative. In their most general form, CIPs include also multiplicity constraints of the type x ≤ d, i.e., arbitrarily large integers are not acceptable in the solution. The multiplicity constraints incur a dichotomy with respect to approximation between (0,1)-CIPs whose matrix A contains only zeros and ones and the general case. Let m denote the number of rows of A. The well known O(log m) cost approximation with respect to the optimum of the linear relaxation is valid for general CIPs, but multiplicity constraints can be dealt with effectively only in the (0,1) case. In the general case, existing algorithms that match the integrality gap for the cost objective violate the multiplicity constraints by a multiplicative O(log m) factor. We make progress by defining column-restricted CIPs, a strict superclass of (0,1)-CIPs, and showing how to find for them integral solutions of cost O(log m) times the LP optimum while violating the multiplicity constraints by a multiplicative O(1) factor.