Decentralized and Self-adaptive Core Maintenance on Temporal Graphs
Davide Rucci, Emanuele Carlini, Patrizio Dazzi, Hanna Kavalionak, Matteo Mordacchini
TL;DR
The paper tackles decentralized maintenance of the $k$-core decomposition in temporal graphs. It introduces a decentralized, iterative, message-passing algorithm that uses a memory-window to accumulate neighborhood information and update coreness as the topology changes. Compared to a centralized baseline based on the static Montresor et al. method, the approach reduces total messages and activated nodes by large factors, with coreness estimates staying within $\pm 1$ of the baseline in practice. The authors validate on large real-world networks and release the implementation to support reproducibility and further study.
Abstract
Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can be effectively modeled through temporal $k$-cores. This paper introduces a novel decentralized and incremental algorithm for computing the core decomposition of temporal networks. Decentralized solutions leverage the ability of network nodes to communicate and coordinate locally, addressing complex problems in a scalable, adaptive, and timely manner. By leveraging previously computed coreness values, our approach significantly reduces the activation of nodes and the volume of message exchanges when the network changes over time. This enables scalability with only a minimal trade-off in precision. Experimental evaluations on large real-world networks under varying levels of dynamism demonstrate the efficiency of our solution compared to a state-of-the-art approach, particularly in terms of active nodes, communication overhead, and convergence speed.