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The Probabilistic Method
The use of randomness is now an accepted tool in Theoretical Computer Science but not everyone is aware of the underpinnings of this methodology in Combinatorics - particularly, in what is now calledExpand
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The Space Complexity of Approximating the Frequency Moments
The frequency moments of a sequence containingmielements of typei, 1?i?n, are the numbersFk=?ni=1mki. We consider the space complexity of randomized algorithms that approximate the numbersFk, whenExpand
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The space complexity of approximating the frequency moments
The frequency moments of a sequence containing mi elements of type i, for 1 i n, are the numbers Fk = P n=1 m k . We consider the space complexity of randomized algorithms that approximate theExpand
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Color-coding
We describe a novel randomized method, the method of color-coding for finding simple paths and cycles of a specified length k, and other small subgraphs, within a given graph G = (V,E). TheExpand
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Eigenvalues and expanders
  • N. Alon
  • Mathematics, Computer Science
  • Comb.
  • 2 January 1986
Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expanderif and only if the second largest eigenvalue of its adjacencyExpand
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Combinatorial Nullstellensatz
We present a general algebraic technique and discuss some of its numerous applications in combinatorial number theory, in graph theory and in combinatorics. These applications include results inExpand
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Colorings and orientations of graphs
Bounds for the chromatic number and for some related parameters of a graph are obtained by applying algebraic techniques. In particular, the following result is proved: IfG is a directed graph withExpand
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A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem
Abstract A simple parallel randomized algorithm to find a maximal independent set in a graph G = ( V , E ) on n vertices is presented. Its expected running time on a concurrent-read concurrent-writeExpand
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Scale-sensitive dimensions, uniform convergence, and learnability
Learnability in Valiant's PAC learning model has been shown to be strongly related to the existence of uniform laws of large numbers. These laws define a distribution-free convergence property ofExpand
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Finding and counting given length cycles
We present an assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs. Most of the bounds obtained depend solely on the number of edges in theExpand
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