Inverse Vertex Obnoxious 1-Center Location Problems

Xiucui Guan, Panos M. Pardalos and Binwu Zhang
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Xiucui Guan: Southeast University
Binwu Zhang: Hohai University

Chapter Chapter 13 in Inverse Combinatorial Optimization Problems, 2025, pp 313-338 from Springer

Abstract: Abstract In this chapter, we first give a brief introduction to the inverse center and median location problems under different norms. Then we mainly consider the inverse vertex obnoxious 1-center location problem (IVO1C) on a general graph G. We aim to adjust the edge weights satisfying upper and lower bounds with the least cost, so that a given vertex s becomes the obnoxious 1-center of graph G. We construct their mathematical models and prove some properties under the weighted l ∞ $$l_\infty $$ norm and bottleneck Hamming distance. We design an O ( n 3 ) $$O(n^3)$$ time algorithm to solve the problem (IVO1C ∞ $$_\infty $$ ) by solving the transcendence point of the cost function in each iteration, where n is the number of vertices in the graph G. We also propose a binary search method for the problem (IVO1C bH $$_{bH}$$ ) with time complexity O ( n 2 log n ) $$O(n^2\log n)$$ . Finally, we show some computational experiments to verify the effectiveness of the algorithms.

Keywords: Inverse center location problems; Inverse median location problems; Inverse vertex obnoxious 1-center location problems; Intersection points of two polyline functions (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-91175-0_13

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DOI: 10.1007/978-3-031-91175-0_13

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