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
Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the power of two-point based sampling
Journal of Complexity
A bridging model for parallel computation
Communications of the ACM
Introduction to algorithms
Realistic analysis of some randomized algorithms
Journal of Computer and System Sciences
Information and Computation
Simulating (logcn)-wise independence in NC
Journal of the ACM (JACM)
An optimal randomized parallel algorithm for finding connected components in a graph
SIAM Journal on Computing
A linear approach to the set maxima problem
SIAM Journal on Discrete Mathematics
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
Optimal randomized algorithms for local sorting and set-maxima
SIAM Journal on Computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Removing randomness in parallel computation without a processor penalty
Journal of Computer and System Sciences
Randomized algorithms and pseudorandom numbers
Journal of the ACM (JACM)
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
Efficient massively parallel implementation of some combinatorial algorithms
Theoretical Computer Science
Finding minimum spanning forests in logarithmic time and linear work using random sampling
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM
Journal of Computer and System Sciences
An optimal EREW PRAM algorithm for minimum spanning tree verification
Information Processing Letters
Efficient approximation of product distributions
Random Structures & Algorithms
On the parallel time complexity of undirected connectivity and minimum spanning trees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Matroid decomposition methods for the set maxima problem
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Information Bounds Are Weak in the Shortest Distance Problem
Journal of the ACM (JACM)
SIAM Journal on Computing
Improved algorithms via approximations of probability distributions
Journal of Computer and System Sciences
The soft heap: an approximate priority queue with optimal error rate
Journal of the ACM (JACM)
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
Expected time bounds for selection
Communications of the ACM
Communications of the ACM
Optimal randomized EREW PRAM algorithms for finding spanning forests
Journal of Algorithms
Randomness efficient identity testing of multivariate polynomials
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Median Selection Requires $(2+\epsilon)n$ Comparisons
SIAM Journal on Discrete Mathematics
A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Minimizing Randomness in Minimum Spanning Tree, Parallel Connectivity, andSet Maxima Algorithms
Minimizing Randomness in Minimum Spanning Tree, Parallel Connectivity, andSet Maxima Algorithms
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Randomized minimum spanning tree algorithms using exponentially fewer random bits
ACM Transactions on Algorithms (TALG)
On Cartesian Trees and Range Minimum Queries
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Research paper: The saga of minimum spanning trees
Computer Science Review
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There are several fundamental problems for which there are optimal randomized algorithms, but whose deterministic complexity remains unresolved. Among such problems are the minimum spanning tree problem, the set maxima problem, the problem of computing connected components and (minimum) spanning trees in parallel and the problem of performing sensitivity analysis on shortest path trees and minimum spanning trees. For each of these problems there is an optimal randomized algorithm which uses a linear number of random bits. We propose new algorithms (or adapt old ones) for these problems which preserve optimality while saving an exponential number of random bits. In the case of computing minimum spanning trees and MST/SSSP sensitivity analysis, we reduce the dependence on randomness to log* n random bits.We also consider the problem of selection, for which we give two algorithms which make an expected 1.5n + o(n) comparisons; one uses O(log n) random bits and is uniform, the other uses O(log log n) random bits and is non-uniform.