One of the most famous results in the theory of random graphs establishes that the threshold for Hamiltonicity in the Erdős-Rényi random graph Gn,p is around p ∼ logn+log logn n . Much research has been done to extend this to increasingly challenging random structures. In particular, a recent result by Frieze determined the asymptotic threshold for a loose Hamilton cycle in the random 3-uniform...

The capability of nodes to broadcast their message to the entire wireless network when nodes employ cooperation is considered. We employ an asymptotic analysis using an extended random network setting and show that the broadcast performance strongly depends on the path loss exponent of the medium. In particular, as the size of the random network grows, the probability of broadcast in a one-dime...

This paper is focussed on algorithms to solve the k-shortest path problem. Three codes were described and compared on rand and grid networks using random generators available on http://www.dis.uniroma1.it/∼challenge9 Codes were also tested on the USA road networks available on the same URL address. One million paths were ranked in less than 3 seconds on random instances with 10 000 nodes and 10...