Using the Pseudo-Dimension to Analyze Approximation Algorithms for Integer Programming

Authors:
Philip M. Long
Affiliations:
-
Venue:
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Year:
2001

Citing 28
Cited 2

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Abstract

We prove approximation guarantees for randomized algorithms for packing and covering integer programs expressed in certain normal forms. The bounds are in terms of the pseudo-dimension of the matrix of the coefficients of the constraints and the value of the optimal solution; they are independent of the number of constraints and the number of variables. The algorithms take time polynomial in the length of the representation of the integer program and the value of the optimal solution. We establish a related result for a class we call the mixed covering integer programs, which contains the covering integer programs. We describe applications of these techniques and results to a generalization of Dominating Set motivated by distributed file sharing applications, to an optimization problem motivated by an analysis of boosting, and to a generalization of matching in hypergraphs.