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The Probabilistic Method
TLDR
A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored. Expand
The space complexity of approximating the frequency moments
TLDR
It turns out that the numbers F0;F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k 6 requires n (1) space. Expand
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
Eigenvalues and expanders
  • N. Alon
  • Computer Science, Mathematics
  • Comb.
  • 2 January 1986
TLDR
It is shown that a regular bipartite graph is an expanderif and only if the second largest eigenvalue of its adjacency matrix is well separated from the first. Expand
Color-coding
TLDR
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), which can be derandomized using families of perfect hash functions. Expand
Colorings and orientations of graphs
TLDR
Bounds for the chromatic number and for some related parameters of a graph are obtained by applying algebraic techniques by proving that there is a legal vertex-coloring of G assigning to each vertexv a color fromS(v). Expand
Finding and counting given length cycles
TLDR
An assortment of methods for finding and counting simple cycles of a given length in directed and undirected graphs improve upon various previously known results. Expand
A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem
TLDR
A technique due to A. Joffe (1974) is applied and deterministic construction in fast parallel time of various combinatorial objects whose existence follows from probabilistic arguments is obtained. Expand
Scale-sensitive dimensions, uniform convergence, and learnability
TLDR
A characterization of learnability in the probabilistic concept model, solving an open problem posed by Kearns and Schapire, and shows that the accuracy parameter plays a crucial role in determining the effective complexity of the learner's hypothesis class. Expand
Simple Construction of Almost k-wise Independent Random Variables
TLDR
This work presents three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent and their simplicity is their simplicity. Expand
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