On the L ∞ -norm of extreme points for crossing supermodular directed network LPs

Authors:
Harold N. Gabow
Affiliations:
University of Colorado at Boulder, Boulder, CO
Venue:
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Year:
2005

Citing 7
Cited 1

Biconnectivity approximations and graph carvings

Journal of the ACM (JACM)
Approximation algorithms

Approximation algorithms
Approximation algorithms for minimum-cost k-vertex connected subgraphs

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A 2-Approximation for Minimum Cost {0, 1, 2} Vertex Connectivity

Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Edge Covers of Setpairs and the Iterative Rounding Method

Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation algorithm for k-node connected subgraphs via critical graphs

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithms for a network design problem with crossing supermodular demands

Networks

Additive guarantees for degree bounded directed network design

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We discuss extensions of Jain's framework for network design [7] that go beyond undirected graphs. The main problem is approximating a minimum cost set of directed edges that covers a crossing supermodular function. We show that iterated rounding gives a factor 3 approximation, where factor 4 was previously known and factor 2 was conjectured. Our bound is tight for the simplest interpretation of iterated rounding. We also show that (the simplest version of) iterated rounding has unbounded approximation ratio when the problem is extended to mixed graphs.