Papers › Uniform Embeddings for Robinson Similarity Matrices
Uniform Embeddings for Robinson Similarity Matrices
Jeannette Janssen, Zhiyuan Zhang
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections