On some inverse 1-center location problems. Nguyen, K. T., Hung, N. T., Nguyen-Thu, H., Le, T. T., & Pham, V. H. Optimization, 68(5):999–1015, 2019. Publisher: Taylor & Francis
On some inverse 1-center location problems [link]Paper  doi  abstract   bibtex   
This paper addresses two problems, the inverse 1-center problem on the line with closed-interval facilities and the inverse 1-center problem on Rd. For the first problem, we develop a combinatorial O(n log n) algorithm based on the convexity of the objective function, where n is the number of facilities. We also discuss the corresponding problem on interval graphs with the similar solution approach. Concerning the inverse 1-center problem on Rd, we propose an O(dn2 log n) algorithm based on the optimality criterion, where n is the number of existing points.
@article{doi:10.1080/02331934.2019.1571056,
	title = {On some inverse 1-center location problems},
	volume = {68},
	issn = {10294945},
	url = {https://doi.org/10.1080/02331934.2019.1571056},
	doi = {10.1080/02331934.2019.1571056},
	abstract = {This paper addresses two problems, the inverse 1-center problem on the line with closed-interval facilities and the inverse 1-center problem on Rd. For the first problem, we develop a combinatorial O(n log n) algorithm based on the convexity of the objective function, where n is the number of facilities. We also discuss the corresponding problem on interval graphs with the similar solution approach. Concerning the inverse 1-center problem on Rd, we propose an O(dn2 log n) algorithm based on the optimality criterion, where n is the number of existing points.},
	number = {5},
	journal = {Optimization},
	author = {Nguyen, Kien Trung and Hung, Nguyen Thanh and Nguyen-Thu, Huong and Le, Tran Thu and Pham, Van Huy},
	year = {2019},
	note = {Publisher: Taylor \& Francis},
	keywords = {1-center, Location problem, interval graph, inverse optimization},
	pages = {999--1015},
}

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