Matching is as easy as matrix inversion
Combinatorica
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
A guided tour of Chernoff bounds
Information Processing Letters
Random pseudo-polynomial algorithms for exact matroid problems
Journal of Algorithms
Randomized Distributed Edge Coloring via an Extension of the Chernoff--Hoeffding Bounds
SIAM Journal on Computing
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Distributions on Level-Sets with Applications to Approximation Algorithms
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
Maximizing submodular set functions subject to multiple linear constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A unified approach to scheduling on unrelated parallel machines
Journal of the ACM (JACM)
Submodular Maximization over Multiple Matroids via Generalized Exchange Properties
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Randomly rounding rationals with cardinality constraints and derandomizations
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximation schemes for multi-budgeted independence systems
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
Dependent Randomized Rounding via Exchange Properties of Combinatorial Structures
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
An Approximation Algorithm for Max-Min Fair Allocation of Indivisible Goods
SIAM Journal on Computing
Fault-tolerant facility location: a randomized dependent LP-Rounding algorithm
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Concentration inequalities for nonlinear matroid intersection
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Efficiency-revenue trade-offs in auctions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Constrained matching problems in bipartite graphs
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Stochastic combinatorial optimization via poisson approximation
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Motivated by multi-budgeted optimization and other applications, we consider the problem of randomly rounding a fractional solution x in the (non-bipartite graph) matching and matroid intersection polytopes. We show that for any fixed δ 0, a given point x can be rounded to a random solution R such that E[1R] = (1 − δ)x and any linear function of x satisfies dimension-free Chernoff-Hoeffding concentration bounds (the bounds depend on δ and the expectation μ). We build on and adapt the swap rounding scheme in our recent work [9] to achieve this result. Our main contribution is a non-trivial martingale based analysis framework to prove the desired concentration bounds. In this paper we describe two applications. We give a randomized PTAS for matroid intersection and matchings with any fixed number of budget constraints. We also give a deterministic PTAS for the case of matchings. The concentration bounds also yield related results when the number of budget constraints is not fixed. As a second application we obtain an algorithm to compute in polynomial time an ∈-approximate Pareto-optimal set for the multi-objective variants of these problems, when the number of objectives is a fixed constant. We rely on a result of Papadimitriou and Yannakakis [26].