Exact Exponential Algorithm for Distance-3 Independent Set Problem

Abstract

Let G=(V,E) be an unweighted simple graph. A distance-d independent set is a subset I ⊆ V such that dist(u, v) ≥ d for any two vertices u, v in I, where dist(u, v) is the distance between u and v. Then, Maximum Distance-d Independent Set problem requires to compute the size of a distance-d independent set with the maximum number of vertices. Even for a fixed integer d ≥ 3, this problem is NP-hard. In this paper, we design an exact exponential algorithm that calculates the size of a maximum distance-3 independent set in O(1.4143ⁿ) time.