quitefastmst Package for R and Python

Euclidean and Mutual Reachability Minimum Spanning Trees

Keywords: Euclidean minimum spanning tree, MST, EMST, mutual reachability distance, nearest neighbours, k-nn, k-d tree, Boruvka, Prim, Jarnik, Kruskal, Genie, HDBSCAN*, DBSCAN, clustering, outlier detection.

Package features:

• Euclidean Minimum Spanning Trees using single-, sesqui-, and dual-tree Borůvka algorithms – quite fast in spaces of low intrinsic dimensionality,

• Minimum spanning trees with respect to mutual reachability distances based on the Euclidean metric (used in the definition of the HDBSCAN* algorithm; see Campello, Moulavi, Sander, 2013),

• Euclidean nearest neighbours with nicely-optimised K-d trees,

• relatively fast fallback algorithms for spaces of higher dimensionality,

• supports multiprocessing via OpenMP (on selected platforms).

Refer to the package homepage at https://quitefastmst.gagolewski.com/ for the reference manual, tutorials, examples, and benchmarks.

Author and maintainer: Marek Gagolewski

Possible applications in topological data analysis: clustering (HDBSCAN*, Genie, Lumbermark, Single linkage, etc.), density estimation, dimensionality reduction, outlier and noise point detection, and many more.

How to Install

Python Version

To install from PyPI, call:

pip3 install quitefastmst  # python3 -m pip install quitefastmst

To learn more about Python, check out my open-access textbook Minimalist Data Wrangling in Python.

For best performance, advanced users will benefit from compiling the package from sources:

CPPFLAGS="-O3 -march=native" pip3 install quitefastmst --force --no-binary="quitefastmst"

🚧 TO DO (help needed): How to enable OpenMP support on macOS/Darwin in setup.py?

R Version

To install from CRAN, call:

install.packages("quitefastmst")

To learn more about R, check out my open-access textbook Deep R Programming.

For best performance, advanced users will benefit from compiling the package from sources:

Sys.setenv(CXX_DEFS="-O3 -march=native")  # for gcc and clang
install.packages("quitefastmst", type="source")

Other

The core functionality is implemented in the form of a C++ library. It can thus be easily adapted for use in other projects.

New contributions are welcome, e.g., Julia, Matlab/GNU Octave wrappers.

License

Copyright (C) 2025–2025 Marek Gagolewski https://www.gagolewski.com/

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License Version 3, 19 November 2007, published by the Free Software Foundation.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License Version 3 for more details. You should have received a copy of the License along with this program. If not, see https://www.gnu.org/licenses/.

References

Borůvka, O., O jistém problému minimálním, Práce Moravské Přírodovědecké Společnosti 3, 1926, 37–58.

Bentley, J.L., Multidimensional binary search trees used for associative searching, Communications of the ACM 18(9), 509–517, 1975, DOI: 10.1145/361002.361007.

Campello, R.J.G.B., Moulavi, D., Zimek, A., Sander, J., Hierarchical density estimates for data clustering, visualization, and outlier detection, ACM Transactions on Knowledge Discovery from Data (TKDD) 10(1), 2015, 1–51, DOI: 10.1145/2733381.

Campello, R.J.G.B., Moulavi, D., Sander, J., Density-based clustering based on hierarchical density estimates, Lecture Notes in Computer Science 7819, 2013, 160–172. DOI: 10.1007/978-3-642-37456-2_14.

Gagolewski, M., Cena, A., Bartoszuk, M., Brzozowski, L., Clustering with minimum spanning trees: How good can it be?, Journal of Classification 42, 2025, 90–112. DOI: 10.1007/s00357-024-09483-1.

Gagolewski, M., A framework for benchmarking clustering algorithms, SoftwareX 20, 2022, 101270. DOI: 10.1016/j.softx.2022.101270. https://clustering-benchmarks.gagolewski.com/.

Jarník, V., O jistém problému minimálním, Práce Moravské Přírodovědecké Společnosti 6, 1930, 57–63.

Maneewongvatana, S., Mount, D.M., It's okay to be skinny, if your friends are fat, The 4th CGC Workshop on Computational Geometry, 1999.

March, W.B., Parikshit, R., Gray, A.G., Fast Euclidean minimum spanning tree: Algorithm, analysis, and applications, Proc. 16th ACM SIGKDD Intl. Conf. Knowledge Discovery and Data Mining (KDD '10), 2010, 603–612.

Olson C.F., Parallel algorithms for hierarchical clustering, Parallel Computing 21(8), 1995, 1313–1325.

McInnes, L., Healy, J., Accelerated hierarchical density-based clustering, IEEE Intl. Conf. Data Mining Workshops (ICMDW), 2017, 33–42, DOI: 10.1109/ICDMW.2017.12.

Prim, R., Shortest connection networks and some generalizations, The Bell System Technical Journal 36(6), 1957, 1389–1401.

Sample, N., Haines, M., Arnold, M., Purcell, T., Optimizing search strategies in K-d Trees, 5th WSES/IEEE Conf. on Circuits, Systems, Communications & Computers (CSCC'01), 2001.

See quitefastmst's homepage for more references.