The algebraic degree of geometric optimization problems
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The geometric median has no closed form for dimension d≥2.
“The geometric median has no closed form for d ≥ 2 (Bajaj, 1988); we compute it via the modified Weiszfeld iteration (Weiszfeld, 1937;Vardi and Zhang, 2000).”
From RoPoLL: Robust Panel of LLM Judges (2026) · cites this paper as Bajaj, 1988
The Introduction (page unavailable) says the planar generalized Weber problem is, in general, not solvable by radicals for five or more points, while noting simple solutions for special configurations. Section 5 (page unavailable) says the unrestricted three-dimensional result is suspected, not proved; the paper proves a result for a line-restricted version. Thus the paper supports the absence of a general radical formula in the planar case, but not the unqualified claim of no closed form for every dimension d ≥ 2. (LLM, conf=0.88)
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Research works printed but not linked: 21
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Cited by
Sorted by citations
RoPoLL: Robust Panel of LLM Judges
Acharya, A., Pan, K. W., & Verkhovsky, B. (2026) · arXiv · doi:10.48550/arxiv.2606.30931
- Authors
- Bajaj, C.
- Affiliations
- Purdue University West Lafayette (US)
- Corresponding author
- Bajaj, Chanderjit
- Venue
- Discrete & Computational Geometry
- Published
- 1988-06
- Volume
- 3
- Issue
- 2
- Pages
- 177-191
- ISSN
- 0179-5376 (ISSN-L)
- 1432-0444
- OpenAlex
- W2071857538
- Cited by
- 200
- References
- 0
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 3 · 2023: 3 · 2022: 4 · 2021: 9 · 2020: 8 · 2019: 7 · 2018: 7 · 2017: 9 · 2016: 13 · 2015: 8 · 2014: 15 · 2013: 12 · 2012: 8
- FWCI
- 0.69
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Discrete & Computational Geometry (publishedVersion)
- Purdue e-Pubs (Purdue University System) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computational Geometry and Mesh Generation
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Keywords
- algebraic degree, Weber problem, Galois theory, computational complexity, geometry optimization, exact algorithms, root extraction
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