While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 − o(1) such a graph has a “giant component” that, given its numbe...
One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a tr...
We present a new approach for designing external graph algorithms and use it to design simple, deterministic and randomized external algorithms for computing connected components, ...
James Abello, Adam L. Buchsbaum, Jeffery Westbrook
We study the random composition of a small family of O(n3 ) simple permutations on {0, 1}n . Specifically we ask what is the number of compositions needed to achieve a permutatio...
Shlomo Hoory, Avner Magen, Steven Myers, Charles R...
In a well-known result Goldreich and Trevisan (2003) showed that every testable graph property has a “canonical” tester in which a set of vertices is selected at random and the...