Influence Maximization on Hypergraphs
ISEF Category: Systems Software
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Subcategory: Algorithms · Difficulty: Advanced · Setup: Home Setup · Time: Full Year
The Hook
A single post can ripple through a whole online group fast. That makes influence maximization a real problem, not just a math puzzle. You are trying to pick the best few starting nodes so a message spreads as far as possible, even when the network has group interactions instead of simple pairs.
What Is It?
Influence maximization asks a simple question: if you can seed a few people with a message, who should you pick so the message spreads the farthest? Think of it like starting a rumor in the right part of a crowd. Pick the wrong people, and the idea stalls. Pick the right people, and it catches fire.
Most basic network models treat connections as pairs, like one person talking to one friend. Hypergraphs are richer. A hyperedge can connect a whole group at once, like a Reddit thread, a group chat, or a cluster of accounts that all react together. That matters because real online spread often happens in groups, not just one-on-one.
Randomized rounding is a way to turn a fractional solution from an optimization model into a real set of chosen nodes. You first solve a relaxed version of the problem, where choices can be split into fractions. Then you round those fractions into a concrete seed set, often with better theory than a plain greedy pick under a tight budget. For your project, you can test whether that method gives better spread, better stability, or better runtime than greedy selection on synthetic or public network data.
Why This Is a Good Topic
This is a strong science fair topic because you can test it with simulation, measure it with clear numbers, and compare it against a standard baseline. The real-world link is easy to explain, since the same idea applies to misinformation, public health messaging, and online marketing. You can learn algorithm design, approximation thinking, graph modeling, and statistical comparison without needing a wet lab.
Research Questions
- How does randomized rounding compare with greedy selection in expected spread under the same seed budget?
- What is the effect of hyperedge size on the advantage of randomized rounding over greedy?
- Does randomized rounding keep its performance when the network has strong community structure?
- To what extent does the seed budget change the gap between the rounded solution and the greedy solution?
- Which diffusion model, independent cascade or threshold-style spread, gives the largest benefit to randomized rounding?
- What is the effect of edge density on runtime and spread quality for each algorithm?
Basic Materials
- Laptop or desktop computer with at least 8 GB RAM.
- Python installed with NumPy, SciPy, NetworkX, and pandas.
- Jupyter Notebook or VS Code for running experiments.
- Public graph datasets from SNAP, KONECT, or other open network repositories.
- Spreadsheet software for logging results and summary tables.
- Basic plotting tool such as Matplotlib or seaborn.
Advanced Materials
- Access to a university or school server for larger simulations.
- Python optimization packages such as CVXPY or PuLP for relaxed formulations.
- Graph partitioning or hypergraph generation tools for synthetic benchmarks.
- A large open social network dataset from SNAP, KONECT, or a similar repository.
- Statistical testing tools in Python, such as SciPy stats or statsmodels.
- Version control with Git for tracking algorithm changes and experiment runs.
Software & Tools
- Python: Runs the simulation, optimization, and result analysis code for your experiment.
- NetworkX: Builds graphs and hypergraph-style structures for testing diffusion rules.
- NumPy: Handles fast array operations and repeated randomized trials.
- pandas: Organizes experiment outputs into clean tables for comparison.
- Matplotlib: Plots spread, runtime, and budget tradeoffs across methods.
Experiment Steps
- Define the exact spread model and decide how your hypergraph will represent group interactions.
- Build a baseline greedy algorithm so you have a direct comparison point.
- Formulate the relaxed optimization problem and choose a randomized rounding rule.
- Decide which network types, budgets, and density levels you will test first.
- Plan how you will measure spread, runtime, and run-to-run stability across many trials.
- Set controls that separate algorithm quality from changes in graph size, structure, or randomness.
Common Pitfalls
- Treating a hypergraph like a normal graph, which hides the group interaction the project is supposed to study.
- Comparing algorithms on different seed budgets, which makes the spread results unfair.
- Running too few randomized trials, which makes the rounding method look unstable just from noise.
- Using only one synthetic graph type, which can make the result depend on one network shape.
- Measuring only final spread and ignoring runtime, which can miss the practical cost of a method that looks better on paper.
What Makes This Competitive
A strong version of this project goes beyond a simple comparison chart. You would test several network structures, report confidence intervals, and show where randomized rounding wins or loses. You could also build a tighter evaluation by checking approximation quality, runtime, and stability across many trials. If your analysis finds a clear pattern tied to budget, community structure, or hyperedge size, the project starts to look much deeper than a classroom demo.
Project Variations
- Test the same algorithm on misinformation-style retweet cascades instead of conversation trees.
- Compare randomized rounding against a local-search or simulated-annealing seed selection method.
- Change the diffusion rule and see whether threshold-based spread or cascade spread favors the rounded solution more.
Learn More
- SNAP: Search the Stanford Large Network Dataset Collection for open graphs and social network benchmarks.
- KONECT: Find network datasets and graph statistics for testing influence spread on real structures.
- PubMed: Search review articles on influence maximization, network diffusion, and misinformation spread.
- MIT OpenCourseWare: Search for algorithms and graph theory course notes on approximation methods and randomized algorithms.
- arXiv: Search for recent preprints on influence maximization in hypergraphs and social networks.