Network Convexity Algorithms via Graph Embeddings

Student: Gavrilev Dmitrii

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Final Grade: 8

Year of Graduation: 2021

In this paper, we propose a new approach for fast convex hull construction for a subset of nodes on a network using graph embeddings. We used the well-known convexity concept in the embedding space to solve a similar problem for geometric learning on graph thus optimizing the process of finding all the shortest paths in the induced subgraph. Several encoder-decoder architectures have been tested, from which the L1 decoder proved to preserve metric characteristics of low convex networks. As a result, it enabled us to search and verify convexity of subgraphs in a faster and more convenient way than standard algorithms on graphs.

Full text (added May 24, 2021)

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