In this work, we study a family of random geometric graphs on hyperbolic spaces. In this setting, N points are chosen randomly on a hyperbolic space and any two of them are joined by an edge with probability that depends on their hyperbolic distance, independently of every other pair. In particular, when the positions of the points have been fixed, the… (More)
We analyze the popular push-pull protocol for spreading a rumor in networks. Initially, a single node knows of a rumor. In each succeeding round, every node chooses a random neighbor, and the two nodes share the rumor if one of them is already aware of it. We present the first theoretical analysis of this protocol on random graphs that have a power law… (More)
Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well-studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random… (More)
—Broadcasting algorithms are of fundamental importance for distributed systems engineering. In this paper we revisit the classical and well-studied push protocol for message broadcasting and we investigate a faulty version of it. Assuming that initially only one node has some piece of information, at each stage every one of the informed nodes chooses… (More)
The paradigm of many choices has influenced significantly the design of efficient data structures and, most notably, hash tables. Cuckoo hashing is a technique that extends this concept. There, we are given a table with n locations, and we assume that each location can hold one item. Each item to be inserted chooses randomly k ≥ 2 locations and has to be… (More)
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards we focus on site percolation where the vertices are retained with probability p. We establish critical values for p… (More)
Chvátal, Rödl, Szemerédi and Trotter  proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform 'pseudo-random' hypergraphs.
A <i>k</i>-uniform hypergraph <i>H</i> = (<i>V, E</i>) is called <i>l</i>-orientable, if there is an assignment of each edge <i>e</i> ε <i>E</i> to one of its vertices <i>v</i> ε <i>e</i> such that no vertex is assigned more than <i>l</i> edges. Let <i>H</i><sub><i>n,m,k</i></sub> be a hypergraph, drawn uniformly at random from the set of all… (More)