[Paper] Enhancing Discrete Particle Swarm Optimization for Hypergraph-Modeled Influence Maximization

Source: arXiv - 2604.15746v1

Overview

The paper introduces a fresh take on the classic influence maximization (IM) problem by modeling social or information networks as hypergraphs—structures that can capture multi‑way (higher‑order) interactions instead of just pairwise links. To tackle the resulting combinatorial explosion, the authors adapt Discrete Particle Swarm Optimization (D‑PSO) with a clever fitness estimator and initialization scheme, delivering a method that consistently beats existing baselines on both synthetic and real‑world hypergraph datasets.

Key Contributions

• Hypergraph‑based IM formulation – moves beyond ordinary graphs to represent group‑wise influences (e.g., a tweet seen by a whole chat group).
• Discrete PSO tailored for seed selection – encodes each particle as a binary vector of seed nodes and defines velocity/position updates suitable for combinatorial search.
• Two‑layer local influence approximation – a fast yet accurate fitness function that estimates cascade spread without running costly full simulations.
• Degree‑based initialization – seeds the swarm with high‑degree hypernodes, giving the optimizer a strong starting point.
• Hybrid local search integration – refines particles after each PSO iteration, accelerating convergence.
• Extensive empirical validation – experiments on multiple synthetic and real hypergraphs show superior spread and runtime compared to state‑of‑the‑art graph‑based and hypergraph‑based baselines.

Methodology

1. Problem Encoding

   • The network is represented as a hypergraph (H = (V, E)) where each hyperedge connects any number of vertices.
   • A particle is a binary vector (x \in {0,1}^{|V|}); a ‘1’ marks a node chosen as a seed.

2. Fitness Evaluation (Two‑layer Approximation)

   • Layer 1: For each seed, compute its immediate hyper‑neighbour influence using node degrees and hyperedge sizes.
   • Layer 2: Aggregate overlapping neighborhoods and apply the classic linear threshold model to estimate the total cascade size.
   • This avoids Monte‑Carlo simulations while preserving the key dynamics of group activation.

3. Swarm Dynamics

   • Velocity is a probabilistic vector indicating the likelihood of flipping each bit, derived from personal best, global best, and inertia terms.
   • Position update samples the binary vector according to the velocity probabilities, ensuring discrete feasibility.

4. Degree‑Based Initialization

   • Seeds are seeded (pun intended) by selecting the top‑k nodes with the highest hyper‑degree (sum of incident hyperedge cardinalities), giving the swarm a high‑quality initial population.

5. Local Search Operator

   • After each PSO iteration, a lightweight greedy tweak examines swapping a seed with a non‑seed that yields the biggest marginal gain in the approximated spread.

6. Algorithm Loop

   • Repeat velocity/position updates → fitness evaluation → local search → update personal/global bests until a stopping criterion (max iterations or convergence) is met.

Results & Findings

• Higher spread: The proposed method consistently achieves a 5‑10 % increase in estimated influence compared to the strongest graph‑based and hypergraph‑based competitors.
• Faster convergence: Thanks to the degree‑based start and local search, the swarm reaches near‑optimal solutions in fewer iterations, cutting runtime by 20‑30 % on large datasets.
• Ablation study: Removing the local search drops performance by ~4 %; using random initialization instead of degree‑based seeding reduces spread by ~3 % and increases iterations needed for convergence.

Practical Implications

• Marketing & Viral Campaigns: Companies can model group‑wise promotions (e.g., bundle discounts, group chats) as hyperedges, then use the algorithm to pick a minimal set of “seed” customers that maximizes word‑of‑mouth reach.
• Social Platform Feature Roll‑outs: Feature flags often target communities (sub‑reddits, Discord servers). Hypergraph‑aware seed selection can accelerate adoption while minimizing rollout cost.
• Network Security: In threat containment, identifying a few critical nodes whose isolation cuts off multi‑party communication can be framed as IM on a hypergraph of communication sessions.
• Tooling: The method is lightweight enough to be wrapped into existing Python/Scala pipelines (e.g., Spark GraphX) as a plug‑in, requiring only the hypergraph adjacency list and a budget k for seeds.

Limitations & Future Work

• Approximation Accuracy: The two‑layer fitness estimator trades exact cascade simulation for speed; in networks with highly non‑linear thresholds, the estimate may diverge from true spread.
• Scalability to Massive Hypergraphs: While experiments covered up to ~50 k nodes, industrial‑scale hypergraphs (millions of nodes, billions of hyperedges) may need distributed PSO variants or further sampling tricks.
• Dynamic Networks: The current formulation assumes a static hypergraph; extending to time‑evolving hyperedges (e.g., trending topics) is an open direction.
• Hybrid Objective Functions: Future work could incorporate cost, fairness, or privacy constraints alongside influence, turning the problem into a multi‑objective optimization.

Bottom line: By marrying a hypergraph view of complex interactions with a tuned discrete PSO engine, the authors deliver a practical, higher‑quality solution to influence maximization—one that developers can start experimenting with today for any application where group dynamics matter.*

Authors

• Qianshi Wang
• Xilong Qu
• Wenbin Pei
• Nan Li
• Qiang Zhang

Paper Information

• arXiv ID: 2604.15746v1
• Categories: cs.SI, cs.NE
• Published: April 17, 2026
• PDF: Download PDF