Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits

DMCA

Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits

Cached

Download Links

Other Repositories/Bibliography

DBLP

by Seth Pettie , Vijaya Ramachandran

Citations:

5 - 1 self

BibTeX

@MISC{Pettie_randomizedminimum,
    author = {Seth Pettie and Vijaya Ramachandran},
    title = {Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits},
    year = {}
}

OpenURL

Abstract

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 the input. In this paper 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 paper — 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,

Keyphrases

random bit minimum spanning tree soft heap many way prominent exception deterministic algorithm mst sensitivity analysis problem local sorting randomized method general method optimal deterministic algorithm karger-klein-tarjan algorithm main focus running time tree problem deterministic minimum spanning tree algorithm wise independent sampler maximum problem many fundamental problem

DMCA