Summary of The Np-hardness Of the Gromov-wasserstein Distance, by Natalia Kravtsova
The NP-hardness of the Gromov-Wasserstein distance
by Natalia Kravtsova
First submitted to arxiv on: 12 Aug 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper investigates the computational complexity of the Gromov-Wasserstein (GW) distance, which is often cited as being NP-hard in literature. To prove this hardness, the authors demonstrate the non-convex nature of the GW optimization problem, showing that it is NP-hard to compute the GW distance between finite spaces for any given input data. The paper provides explicit examples to illustrate this non-convexity. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper explores a challenging mathematical concept called the Gromov-Wasserstein (GW) distance, which is used in various fields like machine learning and computer science. It’s important because it helps us understand how similar two datasets are, even if they have different sizes or structures. The authors prove that this idea is really hard to compute for large datasets, making it a valuable contribution to the field. |
Keywords
» Artificial intelligence » Machine learning » Optimization
