We study the approximation complexity of the Metric Dimension problem in bounded degree, dense as well as in general graphs. For the general case, we prove that the Metric Dimension problem is not approximable within (1 − ǫ) ln n for any ǫ > 0, unless N P ⊆ DT IM E(n log log n), and we give an approximation algorithm which matches the lower bound. Even for… (More)
We give logarithmic lower bounds for the approximability of the Minimum Dominating Set problem in connected (α, β)-Power Law Graphs. We give also a best up to now upper approximation bound on the problem for the case of the parameters β > 2. We develop also a new functional method for proving lower approximation bounds and display a sharp phase transition… (More)
We prove new explicit inapproximability results for the Vertex Cover Problem on the Power Law Graphs and some functional generalizations of that class of graphs. Our results depend on special bounded degree amplifier constructions for those classes of graphs and could be also of independent interest.
In this paper we study the special case of Graphic TSP where the underlying graph is a power law graph (PLG). We give a refined analysis of some of the current best approximation algorithms and show that an improved approximation ratio can be achieved for certain ranges of the power law exponent β. For the value of power law exponent β = 1.5 we obtain an… (More)
We give the first nonconstant lower bounds for the approximability of the Independent Set Problem on the Power Law Graphs. These bounds are of the form n in the case when the power law exponent satisfies β < 1. In the case when β = 1, the lower bound is of the form log(n). The embedding technique used in the proof could also be of independent interest.
In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2 − ζ(β)−1− 1 2 β 2 β ζ(β−1)ζ(β) for random Power Law Graphs (PLG) in the (α, β)-model of Aiello et. al.. We obtain this result by combining the Nemhauser and Trotter approach for Min-VC with a new deterministic… (More)