A fast parallel algorithm for the maximal independent set problem
Journal of the ACM (JACM)
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Probabilistic construction of deterministic algorithms: approximating packing integer programs
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
Constructing a maximal independent set in parallel
SIAM Journal on Discrete Mathematics
Beyond Steiner's problem: a VLSI oriented generalization
WG '89 Proceedings of the fifteenth international workshop on Graph-theoretic concepts in computer science
Simulating (logcn)-wise independence in NC
Journal of the ACM (JACM)
An efficient parallel algorithm that finds independent sets of guaranteed size
SIAM Journal on Discrete Mathematics
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
A parallel approximation algorithm for positive linear programming
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Efficient NC algorithms for set cover with applications to learning and geometry
Proceedings of the 30th IEEE symposium on Foundations of computer science
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Randomized algorithms
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
(De)randomized construction of small samples spaces in NC
Journal of Computer and System Sciences
Rounding via trees: deterministic approximation algorithms for group Steiner trees and k-median
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient approximation of product distributions
Random Structures & Algorithms
A small approximately min-wise independent family of hash functions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A polylogarithmic approximation algorithm for the group Steiner tree problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Improved Approximation Guarantees for Packing and Covering Integer Programs
SIAM Journal on Computing
A matter of degree: improved approximation algorithms for degree-bounded minimum spanning trees
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Low-Bandwidth Routing and Electrical Power Networks
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Solving Some Discrepancy Problems in NC
Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science
Finding large independent sets of hypergraphs in parallel
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
Algorithmic derandomization via complexity theory
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Integrality ratio for group Steiner trees and directed steiner trees
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Partial Covering Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Using the Pseudo-Dimension to Analyze Approximation Algorithms for Integer Programming
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for partial covering problems
Journal of Algorithms
Approximation algorithms for stochastic and risk-averse optimization
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Infrastructure Leasing Problems
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Distributed and parallel algorithms for weighted vertex cover and other covering problems
Proceedings of the 28th ACM symposium on Principles of distributed computing
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
Dynamic programming based algorithms for set multicover and multiset multicover problems
Theoretical Computer Science
Parallel approximation algorithms for facility-location problems
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Energy efficient scheduling via partial shutdown
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
On k-column sparse packing programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Geometric packing under non-uniform constraints
Proceedings of the twenty-eighth annual symposium on Computational geometry
Stochastic vehicle routing with recourse
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Approximating sparse covering integer programs online
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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Covering and packing integer programs model a large family of combinatorial optimization problems. The current-best approximation algorithms for these are an instance of the basic probabilistic method: showing that a certain randomized approach produces a good approximation with positive probability. This approach seems inherently sequential; by employing the method of alteration we present the first RNC and NC approximation algorithms that match the best sequential guarantees. Extending our approach, we get the first RNC and NC approximation algorithms for certain multi-criteria versions of these problems. We also present the first NC algorithms for two packing and covering problems that are not subsumed by the above result: finding large independent sets in graphs, and rounding fractional Group Steiner solutions on trees.