The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
An r-Dimensional Quadratic Placement Algorithm
Abstract
In this paper the solution to the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given. The criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X′X = 1, for each of the r unknown coordinate vectors. It is proved that the problem reduces to the minimization of a sum or r positive semi-definite quadratic forms which, under the quadratic constraints, reduces to the problem of finding r eigenvectors of a special “disconnection” matrix. It is shown, by example, how this can serve as a basis for cluster identification.
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Cites
The Quadratic Assignment Problem
Lawler, E. L. (1963) · Management Science · doi:10.1287/mnsc.9.4.586 · Cited by 964
A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities
Armour, G. C., & Buffa, E. S. (1963) · Management Science · doi:10.1287/mnsc.9.2.294 · Cited by 740
Optimal and Suboptimal Algorithms for the Quadratic Assignment Problem
Gilmore, P. C. (1962) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0110022 · Cited by 448
The Backboard Wiring Problem: A Placement Algorithm
Steinberg, L. (1961) · SIAM Review · doi:10.1137/1003003 · Cited by 379
Quadratic Assignment Problem Algorithms and the Location of Indivisible Facilities
Hillier, F. S., & Connors, M. M. (1966) · Management Science · doi:10.1287/mnsc.13.1.42 · Cited by 231
Cited by
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Structural Properties of the Caenorhabditis elegans Neuronal Network
Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H., & Chklovskii, D. B. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1001066 · Cited by 867
Wiring optimization can relate neuronal structure and function
Chen, B. L., Hall, D. H., & Chklovskii, D. B. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0506806103 · Cited by 650
Schwarzer, G., Carpenter, J. R., & Rücker, G. (2015) · Use R! · doi:10.1007/978-3-319-21416-0_8 · Cited by 109
Spanning Forests of a Digraph and Their Applications
Agaev, R. P., & Chebotarev, P. Y. (2001) · Automation and Remote Control · doi:10.1023/a:1002862312617 · Cited by 57
Metadata
- Authors
- Hall, K. M.
- Venue
- Management Science
- Published
- 1970-11
- Volume
- 17
- Issue
- 3
- Pages
- 219-229
- ISSN
- 0025-1909 (ISSN-L)
- 1526-5501
- OpenAlex
- W2044348081
- Cited by
- 522
- References
- 5
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hall, K. M. (1970). An r-Dimensional Quadratic Placement Algorithm. Management Science. https://doi.org/10.1287/mnsc.17.3.219
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