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- W4283820153 abstract "Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based on quantifying the mismatch between the two graphs, that is, the symmetric difference of the graphs under an optimal alignment of the vertices. An important example is similarity based on graph edit distance. While edit distance calculates the global mismatch, that is, the number of edges in the symmetric difference, our main focus is on local measures calculating the maximum mismatch per vertex. Mathematically, our similarity measures are best expressed in terms of the adjacency matrices: the mismatch between graphs is expressed as the difference of their adjacency matrices (under an optimal alignment), and we measure it by applying some matrix norm. Roughly speaking, global measures like graph edit distance correspond to entrywise matrix norms like the Frobenius norm and local measures correspond to operator norms like the spectral norm. We prove a number of strong NP-hardness and inapproximability results even for very restricted graph classes such as bounded-degree trees." @default.
- W4283820153 created "2022-07-06" @default.
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- W4283820153 date "2022-06-30" @default.
- W4283820153 modified "2023-09-24" @default.
- W4283820153 title "Graph Similarity Based on Matrix Norms" @default.
- W4283820153 doi "https://doi.org/10.48550/arxiv.2207.00090" @default.
- W4283820153 hasPublicationYear "2022" @default.
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