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- Noga Alon, Joel H. Spencer
- SODA
- 1992

- Noga Alon, Yossi Matias, Mario Szegedy
- J. Comput. Syst. Sci.
- 1996

The frequency moments of a sequence containing m i elements of type i, for 1 ≤ i ≤ n, are the numbers F k = n i=1 m k i. We consider the space complexity of randomized algorithms that approximate the numbers F k , when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F 0 , F 1 and F 2 can be… (More)

- Noga Alon, Shai Ben-David, Nicolò Cesa-Bianchi, David Haussler
- J. ACM
- 1993

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 of means to expectations uniformly over classes of random variables. Classes of real-valued functions enjoying such a property are also known as uniform… (More)

- Noga Alon, Raphael Yuster, Uri Zwick
- Algorithmica
- 1997

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 the graph in question, and not on the number of vertices. The bounds obtained improve upon various previously known results.

- Noga Alon, Joel H. Spencer
- SODA '92
- 2000

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 called the probabilistic Method as developed primarily by Paul Erdo&huml;s over the past half century. Here I will explore a particular set of problems - all dealing… (More)

- Noga Alon
- Combinatorica
- 1986

- Noga Alon, Assaf Naor
- STOC
- 2004

The <i>cut-norm</i> ||A||<inf>C</inf> of a real matrix A=(a<inf>ij</inf>)<inf>i∈ R,j∈S</inf> is the maximum, over all I ⊂ R, J ⊂ S of the quantity | Σ<inf>i ∈ I, j ∈ J</inf> a<inf>ij</inf>|. This concept plays a major role in the design of efficient approximation algorithms for dense graph and matrix problems. Here… (More)

- Noga Alon, László Babai, Alon Itai
- J. Algorithms
- 1986

A simple parallel randomized algorithm to find a maximal independent set in a graph G = (V, E) on n vertices is presented. Its expected rmming time on a concurrent-read concurrent-write PRAM with 0(1 E 1 d,,) processors is O(log n), where d,, denotes the maximum degree. On an exclusive-read exclusive-write PRAM with 0(1 El) processors the algorithm runs in… (More)

- Noga Alon, Richard A. Duke, Hanno Lefmann, Vojtech Rödl, Raphael Yuster
- J. Algorithms
- 1994

The Regularity Lemma of Szemer edi is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. Here we rst demonstrate the computational diiculty of nding a regular partition; we show that deciding if a given partition of an input graph satisses the… (More)

- Noga Alon, Michael Tarsi
- Combinatorica
- 1992

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: If G is a directed graph with maximum outdegree d, and if the number of Eulerian subgraphs of G with an even number of edges differs from the number of Eulerian subgraphs with an odd number… (More)