We consider the following variant of the classical random graph process introduced by Erdős and Rényi. Starting with an empty graph on n vertices, choose the next edge uniformly at random among all edges not yet considered, but only insert it if the graph remains planar. We show that for all ε > 0, with high probability, θ(n) edges have to be tested before the number of edges in the graph reach...

In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate such formulas – randomly permute all 2 ` n k ́ possible clauses over the variables x1, . . . , xn, and starting from the empty formula, go over the clauses one by one, including each new clause as you go along if after its addition the formula remains satisfiable. We study the evolution of this proc...

We study a new random search process: the taxi drive. The motivation for this process comes from urban sensing in which sensors are mounted on moving vehicles such as taxis, allowing environments to be opportunistically monitored. Inspired by movements of real drive is composed both and regular parts: passengers brought randomly chosen locations via deterministic (i.e. shortest paths) routes. s...