GreediRIS: Scalable Influence Maximization using Distributed Streaming Maximum Cover

TL;DR

GreediRIS tackles scalable influence maximization by marrying RIS-based sampling with a RandGreedi distributed submodular optimization framework. It reformulates seed selection as a max-$k$-cover problem over RIS samples and introduces streaming aggregation and sender truncation to significantly reduce inter-node communication while preserving approximation guarantees. Empirical results on up to 512 compute nodes demonstrate substantial speedups (up to ~36x for IC and ~29x for LT) with minimal quality loss (~2.72%), and the approach extends to OPIM, illustrating broad applicability to distributed submodular optimization in large-scale graphs. The work offers a general, practical pathway for deploying RIS-based InfMax at scale on modern HPC systems.

Abstract

Influence maximization--the problem of identifying a subset of k influential seeds (vertices) in a network--is a classical problem in network science with numerous applications. The problem is NP-hard, but there exist efficient polynomial time approximations. However, scaling these algorithms still remain a daunting task due to the complexities associated with steps involving stochastic sampling and large-scale aggregations. In this paper, we present a new parallel distributed approximation algorithm for influence maximization with provable approximation guarantees. Our approach, which we call GreediRIS, leverages the RandGreedi framework--a state-of-the-art approach for distributed submodular optimization--for solving a step that computes a maximum k cover. GreediRIS combines distributed and streaming models of computations, along with pruning techniques, to effectively address the communication bottlenecks of the algorithm. Experimental results on up to 512 nodes (32K cores) of the NERSC Perlmutter supercomputer show that GreediRIS can achieve good strong scaling performance, preserve quality, and significantly outperform the other state-of-the-art distributed implementations. For instance, on 512 nodes, the most performant variant of GreediRIS achieves geometric mean speedups of 28.99x and 36.35x for two different diffusion models, over a state-of-the-art parallel implementation. We also present a communication-optimized version of GreediRIS that further improves the speedups by two orders of magnitude.

Figures (5)

• Figure 1: Sampling visualized as a sparse matrix. The sampling phase populates the columns, and the shuffle phase distributes by rows.
• Figure 2: Schematic illustration of our parallel GreediRIS approach inside one round.
• Figure 3: Scaling of the total execution time for our methods GreediRIS and GreediRIS-trunc on up to 512 Perlmutter nodes for input Orkut-group. Also shown is the scaling behavior of the state-of-the-art tool Ripples.
• Figure 4: Parallel runtime breakdown for input LiveJournal (Diffusion model IC) for GreediRIS: by the receiver, sender (longest running), and the total times. Note that in streaming, senders and the receiver run in parallel. The plot corresponding to the receiver shows the breakdown between its communicating thread and bucketing threads. Note that the majority of the SeedSelect time on the receiver is idle time, as senders participate in the all-to-all and then perform their local seed selections.
• Figure 5: Strong scaling plot of GreediRIS (top) and GreediRIS-trunc (bottom) to up to 512 nodes. The seed selection step is shown as the shaded region representing its fraction of the total runtime.

Theorems & Definitions (11)

• Definition 2.1: InfMax
• Definition 2.2: Submodular Function
• Definition 2.3: Random Reverse Reachable (RRR) set
• Theorem 2.1
• Corollary 2.1
• Theorem 3.1
• Lemma 3.1
• proof
• Lemma 3.2
• proof