In an efficient design of routing protocols in ad hoc wireless networks, the connected dominating set (CDS) is widely used as a virtual backbone. To construct the CDS with its size as minimum, many heuristic, meta-heuristic, greedy, approximation and distributed algorithmic approaches have been proposed in the recent years. These approaches mostly concentrated on deriving independent set and th...

we analyze some properties of the distribution $q_{g,k}$ of the first component in a $k$-tuple chosen uniformly‎ ‎in the set of all the $k$-tuples generating a finite group $g$ (the limiting distribution of the product replacement algorithm)‎. ‎in particular‎, ‎we concentrate our attention on‎ ‎the study of the variation distance $beta_k(g)$ between $q_{g,k}$ and the uniform distribution‎. ‎we ...

Abstract We describe a simple deterministic $$O( \varepsilon ^{-1} \log \Delta )$$ O ( ε - 1 log Δ ) round distributed algorithm for $$(2\alpha +...