Minimizing the expense transmission time from the source node to demand nodes - Ghiyasvand, Mehdi; Keshtkar, Iman (Journal of combinatorial optimization, 2024)
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 location problems which are called the f ( σ ) -location and g ( σ ) -location problems. We define an f ( σ ) -location of the network N as a node s ∈ S with the property that the maximum expense transmission time from the node s to the destinations of D is as cheap as possible. The f ( σ ) -location problem divides the range ( 0 , ∞ ) into intervals ∪ i ( a i , b i ) and finds a source s i ∈ S , for each interval ( a i , b i ) , such that s i is a f ( σ ) -location for each σ ∈ ( a i , b i ) . Also, define a g ( σ ) -location as a node s of S with the property that the sum of expense transmission times from the node s to all destinations of D is as cheap as possible. The g ( σ ) -location problem divides the range ( 0 , ∞ ) into intervals ∪ i ( a i , b i ) and finds a source s i ∈ S , for each interval ( a i , b i ) , such that s i is a g ( σ ) -location for each σ ∈ ( a i , b i ) . This paper presents two strongly polynomial time algorithms to solve f ( σ ) -location and g ( σ ) -location problems.