Seeding with Costly Network Information

• 成果类型: Article
• 署名作者: Eckles, Dean; Esfandiari, Hossein; Mossel, Elchanan; Rahimian, M. Amin
• 署名单位: Massachusetts Institute of Technology (MIT); Alphabet Inc.; Google Incorporated; Massachusetts Institute of Technology (MIT); Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2290
• 发表日期: 2022
• 关键词: Social networks; Submodularity

摘要

We study the task of selecting k nodes, in a social network of size n, to seed a diffusion with maximum expected spread size, under the independent cascade model with cascade probability p. Most of the previous work on this problem (known as influence maximization) focuses on efficient algorithms to approximate the optimal seed set with provable guarantees given knowledge of the entire network; however, obtaining full knowledge of the network is often very costly in practice. Here we develop algorithms and guarantees for approximating the optimal seed set while bounding how much network information is collected. First, we study the achievable guarantees using a sublinear influence sample size. We provide an almost tight approximation algorithm with an additive e n loss and show that the squared dependence of sample size on k is asymptotically optimal when e is small. We then propose a probing algorithm that queries edges from the graph and use them to find a seed set with the same almost tight approximation guarantee. We also provide a matching (up to logarithmic factors) lower-bound on the required number of edges. This algorithm is implementable in field surveys or in crawling online networks. Our probing takes p as an input which may not be known in advance, and we show how to down-sample the probed edges to match the best estimate of p if they are collected with a higher probability. Finally, we test our algorithms on an empirical network to quantify the tradeoff between the cost of obtaining more refined network information and the benefit of the added information for guiding improved seeding strategies.