Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
Approximating the throughput of multiple machines under real-time scheduling
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Instant Recognition of Half Integrality and 2-Approximations
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Scan chain design for test time reduction in core-based ICs
ITC '98 Proceedings of the 1998 IEEE International Test Conference
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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We consider a special set covering problem. This problem is a generalization of finding a minimum clique cover in an interval graph. When formulated as an integer program, the 0-1 constraint matrix of this integer program can be partitioned into an interval matrix and a special 0-1 matrix with a single 1 per column. We show that the value of this formulation is bounded by 2k/k+1 times the value of the LP-relaxation, where k is the maximum row sum of the special matrix. For the "smallest" difficult case, i.e., k = 2, this bound is tight. Also we provide an O(n) 3/2 -approximation algorithm in case k = 2.