Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Oles, Vladyslav; Lemons, Nathan; Panchenko, Alexander

doi:10.1007/s10878-024-01202-1

Title: Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Journal Article · 22 August 2024 · Journal of Combinatorial Optimization

DOI: https://doi.org/10.1007/s10878-024-01202-1 · OSTI ID:2437852

; Lemons, Nathan; Panchenko, Alexander

Abstract Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library , and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

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Sponsoring Organization:: USDOE

OSTI ID:: 2437852

Journal Information:: Journal of Combinatorial Optimization, Journal Name: Journal of Combinatorial Optimization Journal Issue: 2 Vol. 48; ISSN 1382-6905

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Country unknown/Code not available

Language:: English

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