Cost-based analyses of random neighbor and derived sampling methods

• Published in: Applied network science Vol. 7; no. 1; pp. 1 - 23
• Main Authors: Novick, Yitzchak, Bar-Noy, Amotz
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2022; Springer Nature B.V; SpringerOpen
• Subjects: Apexes; Complexity; Computer Appl. in Social and Behavioral Sciences; Computer Science; Cost benefit analysis; Costs; Fair cost comparison; Graph theory; High-degree vertex sampling; Methods; Random neighbor sampling; Sampling methods; Science; Simulation and Modeling; Special Issue of the 10th International Conference on Complex Networks and their Applications; High-degree vertex sampling; Random neighbor sampling; Fair cost comparison
• DOI: 10.1007/s41109-022-00475-x
• ISSN: 2364-8228

Random neighbor sampling, or RN , is a method for sampling vertices with a mean degree greater than that of the graph. Instead of naïvely sampling a vertex from a graph and retaining it (‘random vertex’ or RV ), a neighbor of the vertex is selected instead. While considerable research has analyzed various aspects of RN , the extra cost of sampling a second vertex is typically not addressed. This paper explores RN sampling from the perspective of cost. We break down the cost of sampling into two distinct costs, that of sampling a vertex and that of sampling a neighbor of an already sampled vertex, and we also include the cost of actually selecting a vertex/neighbor and retaining it for use rather than discarding it. With these three costs as our cost-model, we explore RN and compare it to RV in a more fair manner than comparisons that have been made in previous research. As we delve into costs, a number of variants to RN are introduced. These variants improve on the cost-effectiveness of RN in regard to particular costs and priorities. Our full cost-benefit analysis highlights strengths and weaknesses of the methods. We particularly focus on how our methods perform for sampling high-degree and low-degree vertices, which further enriches the understanding of the methods and how they can be practically applied. We also suggest ‘two-phase’ methods that specifically seek to cover both high-degree and low-degree vertices in separate sampling phases.