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- W4288282947 abstract "A subset of vertices in a graph is called resolving when the geodesic distances to those vertices uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of Hamming graphs in terms of a constrained linear system and deduce a novel but straightforward characterization of resolvability for hypercubes. We propose an integer linear programming method to assess resolvability rapidly, and provide a more costly but definite method based on Grobner bases to determine whether or not a set of vertices resolves an arbitrary Hamming graph. As proof of concept, we identify a resolving set of size 77 in the metric space of all octapeptides (i.e., proteins composed of eight amino acids) with respect to the Hamming distance; in particular, any octamer may be readily represented as a 77-dimensional real-vector. Representing k-mers as low-dimensional numerical vectors may enable new applications of machine learning algorithms to symbolic sequences." @default.
- W4288282947 created "2022-07-28" @default.
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- W4288282947 date "2019-07-12" @default.
- W4288282947 modified "2023-09-29" @default.
- W4288282947 title "Resolvability of Hamming Graphs" @default.
- W4288282947 doi "https://doi.org/10.48550/arxiv.1907.05974" @default.
- W4288282947 hasPublicationYear "2019" @default.
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