Combinatorial Algorithms for the Uniform-Cost Inverse 1-Center Problem on Weighted Trees
Kien Trung Nguyen
,
Huong Nguyen-Thu
,
Nguyen Thanh Hung
Inverse 1-center problem on a network is to modify the edge lengths or vertex weights within certain bounds so that the prespecified vertex becomes an (absolute) 1-center of the perturbed network and the modifying cost is minimized. This paper focuses on the inverse 1-center problem on a weighted tree with uniform cost of edge length modification, a generalization for the analogous problem on an unweighted tree (Alizadeh and Burkard, Discrete Appl. Math. 159, 706–716, 2011). To solve this problem, we first deal with the weighted distance reduction problem on a weighted tree. Then, the weighted distances balancing problem on two rooted trees is introduced and efficiently solved. Combining these two problems, we derive a combinatorial algorithm with complexity of
Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam
Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội
Điện thoại: 024 37563474 - Fax: 024 37564303
Email: vientoan@math.ac.vn
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