A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for a Directed Network Design Problem
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On the L ∞ -norm of extreme points for crossing supermodular directed network LPs
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
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Given a digraph G = (V,E), we study a linear programming relaxation of the problem of finding a minimum-cost edge cover of pairs of sets of nodes (called setpairs), where each setpair has a nonnegative integer-valued demand. Our results are as follows: (1) An extreme point of the LP is characterized by a noncrossing family of tight setpairs, L (where |L| ≤ |E|). (2) In any extreme point x, there exists an edge e with xe ≥ Θ(1)/√|L|, and there is an example showing that this lower bound is best possible. (3) The iterative rounding method applies to the LP and gives an integer solution of cost O(√|L|) = O(√|E|) times the LP's optimal value. The proofs rely on the fact that L can be represented by a special type of partially ordered set that we call diamond-free.