Reconstructing a cascade from temporal observations

TL;DR

This paper introduces algorithms for reconstructing information cascades in networks using temporal activation data, formulating it as a Steiner-tree problem, and demonstrates improved accuracy and scalability on real-world networks.

Contribution

It formulates cascade reconstruction with temporal data as a Steiner-tree variant and provides three approximation algorithms with proven guarantees and scalability.

Findings

Temporal information improves cascade reconstruction accuracy.

The best algorithm achieves an O(√k)-approximation guarantee.

Algorithms are effective on large real-world networks.

Abstract

Given a subset of active nodes in a network can we re- construct the cascade that has generated these observa- tions? This is a problem that has been studied in the literature, but here we focus in the case that tempo- ral information is available about the active nodes. In particular, we assume that in addition to the subset of active nodes we also know their activation time. We formulate this cascade-reconstruction problem as a variant of a Steiner-tree problem: we ask to find a tree that spans all reported active nodes while satisfying temporal-consistency constraints. We present three approximation algorithms. The best algorithm in terms of quality achieves a O(\sqrt{k})-approximation guarantee, where k is the number of active nodes, while the most efficient algorithm has linearithmic running time, making it scalable to very large graphs. We evaluate our algorithms on real-world networks with both simulated and real cascades. Our results in- dicate that utilizing the available temporal information allows for more accurate cascade reconstruction. Fur- thermore, our objective leads to finding the "backbone" of the cascade and it gives solutions of high precision.