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- W3161090734 abstract "A Robinson similarity matrix is a symmetric matrix where the entry values on all rows and columns increase toward the diagonal. Decompose the Robinson matrix into the sum of k {0, 1}-matrices, then these k {0, 1}-matrices are the adjacency matrices of a set of nested unit interval graphs. Previous studies show that unit interval graphs coincide with indifference graphs. An indifference graph has an embedding that maps each vertex to a real number, where two vertices are adjacent if their embedding is within a fixed threshold distance. In this thesis, consider k different threshold distances, we study the problem of finding an embedding that, simultaneously and with respect to each threshold distance, embeds the k indifference graphs corresponding to the k adjacency matrices. This is called a uniform embedding of a Robinson matrix with respect to the k threshold distances. We give a sufficient and necessary condition on Robinson matrices that have a uniform embedding, which is derived from paths in an associated graph. We also give an efficient combinatorial algorithm to find a uniform embedding or give proof that it does not exist, for the case where k = 2." @default.
- W3161090734 created "2021-05-24" @default.
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- W3161090734 date "2021-05-19" @default.
- W3161090734 modified "2023-09-24" @default.
- W3161090734 title "Uniform Embeddings for Robinson Similarity Matrices" @default.
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- W3161090734 doi "https://doi.org/10.48550/arxiv.2105.09197" @default.
- W3161090734 hasPublicationYear "2021" @default.
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