A Fair-Cost Analysis of the Random Neighbor Sampling Method

Random neighbor sampling, or RN, is a method for sampling vertices with an average degree greater than the mean degree of the graph. It samples a vertex, then exchanges it for one of its neighbors which is assumed to be of higher degree. While considerable research has analyzed various aspects of RN, the extra cost of sampling a second vertex is typically not addressed. In this paper, we offer an analysis of RN from the perspective of cost. We define three separate costs, the cost of sampling a vertex, the cost of sampling a neighbor, and the cost of selecting a vertex (as opposed to discarding it in exchange for another). We introduce variations to RN, RVN which retains the first sampled vertex, and RN-RV and RVN-RV which are 'hybrid' methods that sample differently in two separate phases. We study all of these methods in terms of the costs we define. The cost-benefit analysis highlights the methods' strengths and weaknesses, with a specific focus on their respective performances for finding high-degree vs. low-degree vertices. The analyses and results provide a far richer understanding of RN and open a new area of exploration for researching additional sampling methods that are best suited for cost-effectiveness in light of particular goals.