Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
— In this paper, we propose a novel duty cycling algorithm for large-scale dense wireless sensor networks. The proposed algorithm is based on a social behavior of nodes in the se...
We give tight bounds on the parallel complexity of some problems involving random graphs. Speci cally, we show that a Hamiltonian cycle, a breadth rst spanning tree, and a maximal...
Let L be chosen uniformly at random from among the latin squares of order n 4 and let r, s be arbitrary distinct rows of L. We study the distribution of r,s, the permutation of t...
Nicholas J. Cavenagh, Catherine S. Greenhill, Ian ...
Abstract. Random sampling is an important tool in the design of parallel algorithms. Using random sampling it is possible to obtain simple parallel algorithms which are e cient in ...