Inapproximability of Dominating Set in Power Law Graphs

TL;DR

This paper establishes logarithmic lower bounds and improved upper bounds for approximating the Minimum Dominating Set in power law graphs, revealing a phase transition in approximability.

Contribution

It introduces a new functional method for proving lower bounds and characterizes the phase transition in approximability for the problem.

Findings

Logarithmic lower bounds for approximability in power law graphs.

Improved upper approximation bounds for beta>2.

Identification of a sharp phase transition in the problem's approximability.

Abstract

We give logarithmic lower bounds for the approximability of the Minimum Dominating Set problem in connected (alpha,beta)-Power Law Graphs. We give also a best up to now upper approximation bound on the problem for the case of the parameters beta>2. We develop also a new functional method for proving lower approximation bounds and display a sharp phase transition between approximability and inapproximability of the underlying problem. This method could also be of independent interest.