In view of some shortcomings of traditional vertex 1-center (V1C), we introduce a vertex
quickest 1-center (VQ1C) problem on a tree, which aims to find a vertex such that the …

We address the problem of modifying vertex weights of a block graph at minimum total cost
so that a predetermined set of p connected vertices becomes a connected p-median on the …

We consider in this paper the inverse 1-median problem on trees with variable vertex
weights, which are partitioned into groups. While the modifications in each group are …

The concept of the quickest path refers to the path with the minimum transmission time,
considering both its length and capacity. We investigate the problem of finding a point on a …

The theory of inverse location involves modifying parameters in such a way that the total cost
is minimized and one/several prespecified facilities become optimal based on these …

Inverse optimization is the study of imputing unknown model parameters of an optimization
problem using past observed solutions to that problem. In inverse linear programming …

In this paper, we propose a unified approach to solving the inverse 1-median problem on
trees under both the sum and max objectives by using the ordered median function. For the …

Given an undirected tree T=(V, E) and a value σ> 0, every edge e∈ E has a lead time l (e)
and a capacity c (e). Let P st be the unique path connecting s and t. A transmission time of …

An undirected graph G=(V, A) by a set V of n nodes, a set A of m edges, and two sets S, D⊆
V consists of source and demand nodes are given. This paper presents two new versions of …

In location theory, group median generalizes the concepts of both median and center. We
address in this paper the problem of modifying vertex weights of a tree at minimum total cost …