The power of 2 choices over preferential attachment

TL;DR

This paper introduces a preferential attachment model with a choice mechanism, where new vertices connect to the smaller degree vertex among two options, and analyzes the maximum degree growth with high probability.

Contribution

It presents a novel preferential attachment process incorporating a choice rule and provides probabilistic bounds on the maximum degree.

Findings

Largest degree is tightly bounded with high probability.

The model exhibits different growth dynamics compared to standard preferential attachment.

Choice mechanism influences the degree distribution significantly.

Abstract

We introduce a new type of preferential attachment tree that includes choices in its evolution, like with Achlioptas processes. At each step in the growth of the graph, a new vertex is introduced. Two possible neighbor vertices are selected independently and with probability proportional to degree. Between the two, the vertex with smaller degree is chosen, and a new edge is created. We determine with high probability the largest degree of this graph up to some additive error term.