# Inverse 1-median Problem on Trees under Weighted l ∞  Norm

• Xiucui Guan
• Binwu Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)

## Abstract

The inverse 1-median problem is concerned with modifying the weights of the customers at minimum cost such that a prespecified supplier becomes the 1-median of modified location problem. We first present the model of inverse 1-median problem on trees. Then we propose two algorithms to solve the problem under weighted l  ∞  norm with bound constraints on modifications. Based on the approach of the unbounded case, we devise a greedy-type algorithm which runs in O(n 2) time, where n is the number of vertices. Based on the property of the optimal solution, we propose an O(n logn) time algorithm using the binary search.

## Keywords

Inverse 1-median problem Tree weighted l ∞  norm Binary search

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