Lower Bounds and Algorithms for Dominating Sets in Web Graphs
Abstract
In this paper we study the size of dominating sets, and their generalizations, in two graph processes which are widely used to model aspects of the world-wide web. In these processes each new vertex connects to the existing graph by a constant number, $m$, of edges. The terminal vertices of these edges are chosen uniformly at random or by preferential attachment depending on the process. We show that almost all such graph processes have minimal dominating sets linear in the size of the graph and give bounds for this size as a function of $m$. We obtain the upper bounds from simple on-line algorithms for dominating sets. The lower bounds are obtained by proving that the lexicographically first set of a given size is the most likely to dominate.
Domains
Other [cs.OH]
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