The network-untangling problem : from interactions to activity timelines

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Rozenshtein , P , Tatti , N & Gionis , A 2021 , ' The network-untangling problem : from interactions to activity timelines ' , Data Mining and Knowledge Discovery , vol. 35 , pp. 213–247 .

Title: The network-untangling problem : from interactions to activity timelines
Author: Rozenshtein, Polina; Tatti, Nikolaj; Gionis, Aristides
Contributor organization: Department of Computer Science
Helsinki Institute for Information Technology
Date: 2021
Language: eng
Number of pages: 35
Belongs to series: Data Mining and Knowledge Discovery
ISSN: 1384-5810
Abstract: 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) is an element of E denotes 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 and k > 1 activity intervals per entity. For the case 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, we show that both formulations are inapproximable. However, wepropose 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.
Subject: Temporal networks
Complex networks
Timeline reconstruction
Vertex cover
Linear programming
113 Computer and information sciences
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: acceptedVersion

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