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

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 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, when… Expand

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

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

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

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 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

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

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