Best Bang for the Buck: Cost-Effective Seed Selection for Online Social Networks

Abstract

We study the min-cost seed selection problem in online social networks, where the goal is to select a set of seed nodes with the minimum total cost such that the expected number of influenced nodes in the network exceeds a predefined threshold. We propose several algorithms that outperform the state-of-the-art algorithms both theoretically and experimentally. Under the case where the users have heterogeneous costs, our algorithms are the first bi-criteria approximation algorithms with polynomial running time and provable logarithmic performance bounds using a general contagion model. Under the case where the users have uniform costs, our algorithms achieve logarithmic approximation ratio and provable time complexity which is smaller than that of existing algorithms in orders of magnitude. We conduct extensive experiments using real social networks. The experimental results show that, our algorithms significantly outperform the existing algorithms both on the total cost and on the running time, and also scale well to billion-scale networks.

Efficient Approximation Algorithms for Adaptive Seed Minimization

“…Specifically, ATEUC selects two seed set candidates S u and S l , which are taken as the upper bound and lower bound on the number of seed nodes in the optimal ATEUC ASTI ASTI-4 ASTI-2 ASTI-8 ADAPTIM solution. Only when the condition |S u | ≤ 2|S l | is satisfied, the candidate set S u is returned as the solution; otherwise ATEUC will continue to refine S u and S l [22]. The larger the threshold, the more seed nodes are required, and the more easily this stop condition is met, which explains the unique running time pattern of ATEUC.…”

“…Algorithms. We evaluate six algorithms: ASTI, ASTI-2, ASTI-4, ASTI-8, AdaptIM and ATEUC [22]. ASTI-b is ASTI instantiated by TRIM-B with the batch sizes of b.…”

“…Following the common setting in the literature [1,41], we set the approximation parameter ε = 0.5 for the five adaptive algorithms. For those parameters in ATEUC, we use the values recommended in [22]. For each dataset, we set the edge probability p(⟨u, v⟩)…”

“…Existing work on seed minimization mostly focuses on the non-adaptive setting [19,22,47], which requires that all seed nodes should be selected in one batch without observing the actual influence of any node, i.e., no randomness in the influence propagation process can be removed until all seed nodes are fixed. As a consequence of the non-adaptiveness, these solutions may return a seed set that fails to influence at least η nodes in the actual propagation process, or may select an excessive number of seed nodes that generate an actual influence spread much larger than required.…”

Efficient adaptive approximation algorithms in online social networks

“…As a dual problem of influence maximization problem, the seed minimization (SM) problem asks for the minimum number of seed nodes to influence at least a required number η of users, taking into account the randomness in the influence propagation process. Existing work on seed minimization mostly focuses on the non-adaptive setting [5,23,24], which requires that all seed nodes should be selected in one batch without observing the actual influence of any node, i.e., no randomness in the influence propagation process can be removed until all seed nodes are fixed. As a consequence of the non-adaptiveness, these solutions may return a seed set that fails to influence at least η nodes in the actual propagation process, or may select an excessive number of seed nodes that generate an actual influence spread much larger than required.…”