Optimal Dynamic Subset Sampling: Theory and Applications

We study the fundamental problem of sampling independent events, called subset sampling. Specifically, consider a set of \(n\) events \(S=\{x_1, \ldots, x_n\}\), where each event \(x_i\) has an associated probability \(p(x_i)\). The subset sampling problem aims to sample a subset \(T \subseteq S\),...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org
Hauptverfasser: Lu, Yi, Wang, Hanzhi, Wei, Zhewei
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 21.09.2023
Schlagworte:
Algorithms
Data structures
Evolution
Lower bounds
Maximization
Optimization
Sampling
Social networks
ISSN:2331-8422
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We study the fundamental problem of sampling independent events, called subset sampling. Specifically, consider a set of \(n\) events \(S=\{x_1, \ldots, x_n\}\), where each event \(x_i\) has an associated probability \(p(x_i)\). The subset sampling problem aims to sample a subset \(T \subseteq S\), such that every \(x_i\) is independently included in \(S\) with probability \(p_i\). A naive solution is to flip a coin for each event, which takes \(O(n)\) time. However, the specific goal is to develop data structures that allow drawing a sample in time proportional to the expected output size \(\mu=\sum_{i=1}^n p(x_i)\), which can be significantly smaller than \(n\) in many applications. The subset sampling problem serves as an important building block in many tasks and has been the subject of various research for more than a decade. However, most of the existing subset sampling approaches are conducted in a static setting, where the events or their associated probability in set \(S\) is not allowed to be changed over time. These algorithms incur either large query time or update time in a dynamic setting despite the ubiquitous time-evolving events with changing probability in real life. Therefore, it is a pressing need, but still, an open problem, to design efficient dynamic subset sampling algorithms. In this paper, we propose ODSS, the first optimal dynamic subset sampling algorithm. The expected query time and update time of ODSS are both optimal, matching the lower bounds of the subset sampling problem. We present a nontrivial theoretical analysis to demonstrate the superiority of ODSS. We also conduct comprehensive experiments to empirically evaluate the performance of ODSS. Moreover, we apply ODSS to a concrete application: influence maximization. We empirically show that our ODSS can improve the complexities of existing influence maximization algorithms on large real-world evolving social networks.
Bibliographie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2305.18785