The network-untangling problem: from interactions to activity timelines

• Autores: Polina Rozenshtein, Nikolaj Tatti, Aristides Gionis
• Localización: Data mining and knowledge discovery, ISSN 1384-5810, Vol. 35, Nº 1, 2021, págs. 213-247
• Idioma: inglés
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• Resumen

  • In this paper we study a problem of determining when entities are active based on their interactions with each other. We consider a set of entities V and a sequence of time-stamped edges E among the entities. Each edge $$(u,v,t)\in E$$(u,v,t)∈Edenotes an interaction between entities u and v at time t. We assume an activity model where each entity is active during at most k time intervals. An interaction (u, v, t) can be explained if at least one of u or v are active at time t. Our goal is to reconstruct the activity intervals for all entities in the network, so as to explain the observed interactions. This problem, the network-untangling problem, can be applied to discover event timelines from complex entity interactions. We provide two formulations of the network-untangling problem: (i) minimizing the total interval length over all entities (sum version), and (ii) minimizing the maximum interval length (max version). We study separately the two problems for $$k=1$$k=1and $$k>1$$k>1activity intervals per entity. For the case $$k=1$$k=1, we show that the sum problem is NP-hard, while the max problem can be solved optimally in linear time. For the sum problem we provide efficient algorithms motivated by realistic assumptions. For the case of $$k>1$$k>1, we show that both formulations are inapproximable. However, we propose efficient algorithms based on alternative optimization. We complement our study with an evaluation on synthetic and real-world datasets, which demonstrates the validity of our concepts and the good performance of our algorithms.