We study thresholds for Ramsey properties of random discrete structures. In particular, we determine the threshold for Rado's theorem for solutions of partition regular systems of equations in rand...

In this article, we analyze the appearance of a Hamilton cycle in the following random process. The process starts with an empty graph on nlabeled vertices. At each round we are presented with K = ...

The behavior of the random graph G(n,p) around the critical probability pc = $ {1 \over n} $ is well understood. When p = (1 + O(n1-3))pc the components are roughly of size n2-3 and converge, when ...

We establish central and local limit theorems for the number of vertices in the largest component of a random d-uniform hypergraph Hd(n,p) with edge probability p = c-$\left(\matrix{n-1 \cr d-1 }\r...

We consider in this article the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected...

In this article we consider tries built from n strings such that each string can be chosen from a pool of k strings, each of them generated by a discrete i.i.d. source. Three cases are considered: k = 2, k is large but fixed, and k ~ clog n. The goal in each case is to obtain tries as balanced as possible. Various parameters such as height and fill-up level are analyzed. It is shown that for two-choice tries a 50% reduction in height is achieved when compared with ordinary tries. In a greedy online construction when the string that minimizes the depth of insertion for every pair is inserted, the height is only reduced by 25p. To further reduce the height by another 25%, we design a more refined online algorithm. The total computation time of the algorithm is O(nlog n). Furthermore, when we choose the best among k ≥ 2 strings, then for large but fixed k the height is asymptotically equal to the typical depth in a trie. Finally, we show that further improvement can be achieved if the number of choices for each string is proportional to log n. In this case highly balanced trees can be constructed by a simple greedy algorithm for which the difference between the height and the fill-up level is bounded by a constant with high probability. This, in turn, has implications for distributed hash tables, leading to a randomized ID management algorithm in peer-to-peer networks such that, with high probability, the ratio between the maximum and the minimum load of a processor is O(1). © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009

Caching is widely recognized as an effective mechanism for improving the performance of the World Wide Web. One of the key components in engineering the Web caching systems is designing document pl...

The JohnsonLindenstrauss lemma asserts that an n-point set in any Euclidean space can be mapped to a Euclidean space of dimension k = O(e-2 log n) so that all distances are preserved up to a multip...

A standard technique from the hashing literature is to use two hash functions h1(x) and h2(x) to simulate additional hash functions of the form gi(x) = h1(x) + ih2(x). We demonstrate that this tech...

We study the simple random walk on the n-dimensional hypercube, in particular its hitting times of large (possibly random) sets. We give simple conditions on these sets ensuring that the properly r...