Work

An O(kn)-Time Algorithm to Solve Steiner (k, k′)-Eccentricity on Trees

Year: 2025

Type: article

Abstract: Steiner (k,k′)-eccentricity on a given fixed k′-subset in a graph G is the maximum Steiner distance over all k-subsets of V(G) which contain the fixed k′-set, where the Steiner distance of a set is the size of a minimum Steiner tree on this set in a graph. Let R⊆V(T) be the given fixed k′-subset in a tree T. Let k1 and k2 be two integers such that k1≥k2≥k′. We prove that, in a tree, every optimal solution of Steiner (k1,k′)-eccentricity on R takes some optimal solution of Steiner (k2,k′)-eccentricity on R as a partial solution. On the other hand, every optimal solution of Steiner (k2,k′)-eccentricity on R is part of some optimal solution of Steiner (k1,k′)-eccentricity on the set R in a tree. Finally, we present an O(kn)-time algorithm to solve Steiner (k,k′)-eccentricity on a given fixed k′-set in trees.

Source: Axioms

DOI: 10.3390/axioms14030166

Author: Xingfu Li

Institution: Guizhou University of Finance and Economics

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Guizhou Science and Technology Department