Deterministic simulation in LOGSPACE
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Efficient implementation of graph algorithms using contraction
Journal of the ACM (JACM)
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Introduction to algorithms
Information and Computation
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
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
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Randomized algorithms
Chernoff-Hoeffding Bounds for Applications with Limited Independence
SIAM Journal on Discrete Mathematics
Algorithmic number theory
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
Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
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
Concurrent threads and optimal parallel minimum spanning trees algorithm
Journal of the ACM (JACM)
Optimal randomized EREW PRAM algorithms for finding spanning forests
Journal of Algorithms
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A Randomized Time-Work Optimal Parallel Algorithm for Finding a Minimum Spanning Forest
SIAM Journal on Computing
Median Selection Requires $(2+\epsilon)n$ Comparisons
SIAM Journal on Discrete Mathematics
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
Finding Minimum Spanning Trees in O(m alpha(m,n)) Time
On the shortest path and minimum spanning tree problems
On the shortest path and minimum spanning tree problems
Sensitivity analysis of minimum spanning trees in sub-inverse-ackermann time
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A simpler implementation and analysis of Chazelle's soft heaps
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Proceedings of the 14th International Conference on Extending Database Technology
An effective and efficient parallel approach for random graph generation over GPUs
Journal of Parallel and Distributed Computing
A quasi-polynomial time partition oracle for graphs with an excluded minor
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best-known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear, running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of input. In this article we develop some general methods for reducing exponentially the consumption of random bits in comparison-based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant, without affecting the expected running time. Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or O(1)-wise independent sampler. The prominent exception, and the main focus of this article, is a linear-time randomized minimum spanning tree algorithm that is not derived from the well-known Karger-Klein-Tarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on soft heaps. Further, using our algorithm as a guide, we present a unified view of the existing “nongreedy” minimum spanning tree algorithms. Concepts from the Karger-Klein-Tarjan algorithm, such as F-lightness, MST verification, and sampled graphs, are related to the concepts of edge corruption, subgraph contractibility, and soft heaps, which are the basis of the deterministic MST algorithms of Chazelle and Pettie-Ramachandran.