Sparsification of Compact Ultrametrics
DOI:
https://doi.org/10.31471/2304-7399-2026-22(83)-67-75Keywords:
Ultrametric, binary tree, Haar basisAbstract
We introduce and study a relation of refinement between compact ultrametrics. Efficient methods to determine ultrametrics by functions on binary trees and by symmetric bilinear forms that attain a diagonal form in a basis of Haar-like wavelets, are also proposed.
References
1. E. Gorman, M.E. Lladser, Sparsification of large ultrametric matrices: insights into the microbial Tree of Life, Proc. R. Soc. A, 479: 20220847 (2023). https://doi.org/10.1098/rspa.2022.0847
2. M. Krötzsch, Generalized ultrametric upaces in quantitative domain theory, Theor. Comput. Sci., 368, 30-49 (2006). https://doi.org/10.1016/j.tcs.2006.05.037
3. S.G.Mallat, A wavelet tour of signal processing: the sparse way. Orlando, FL: Elsevier/Academic Press, 2009.
4. S. Nykorovych, O. Nykyforchyn, Metric and Topology on the Poset of Compact Pseudoultrametrics, Carpathian Math. Publ, 15:2, 321–330 (2023). https://doi.org/10.15330/cmp.15.2.321-330
5. N. Uglešić, On ultrametrics and equivalence relations — duality, International Mathematical Forum. 5:21, 1037–1048(1978).
6. R.S. Varga, R. Nabben, On Symmetric Ultrametric Matrices, in: Numerical Linear Algebra, Berlin, New York: De Gruyter, pp. 193–200 (1993). https://doi.org/10.1515/9783110857658.193
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Copyright (c) 2026 Олег Никифорчин, Volodymyr Penhryn
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