Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
SIAM Journal on Computing
On the complexity of approximating k-set packing
Computational Complexity
Approximating minimum bounded degree spanning trees to within one of optimal
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Multicommodity demand flow in a tree and packing integer programs
ACM Transactions on Algorithms (TALG)
Mathematics of Operations Research
Unsplittable Flow in Paths and Trees and Column-Restricted Packing Integer Programs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Distributed fractional packing and maximum weighted b-matching via tail-recursive duality
DISC'09 Proceedings of the 23rd international conference on Distributed computing
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximability of Sparse Integer Programs
Algorithmica - Special Issue: European Symposium on Algorithms, Design and Analysis
Greedy approximation via duality for packing, combinatorial auctions and routing
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems, no single method has emerged that matches the effectiveness and simplicity afforded by the covering case. We offer a simple iterative packing technique that retains features of Jain's seminal approach, including the property that the magnitude of the fractional value of the element rounded during each iteration has a direct impact on the approximation guarantee. We apply iterative packing to generalized matching problems including demand matching and k-column-sparse column-restricted packing (k-CS-PIP) and obtain approximation algorithms that essentially settle the integrality gap for these problems. We present a simple deterministic 2k-approximation for k-CSPIP, where an 8k-approximation was the best deterministic algorithm previously known. The integrality gap in this case is at least 2(k-1+1/k). We also give a deterministic 3-approximation for a generalization of demand matching, settling its natural integrality gap.