A Generalization of Distance Domination

TL;DR

This paper introduces a quadratic-complexity algorithm for a generalized distance domination problem in trees, aiming to optimize service center placement and reduce redundancy in network coverage.

Contribution

It extends existing graph theory concepts with a new algorithm for minimum failure-set cardinality in trees, addressing practical service and redundancy issues.

Findings

Developed a quadratic-time algorithm for the generalized problem

Demonstrated applications in service center location optimization

Reduced redundancy in distance-based network coverage

Abstract

Expanding on the graph theoretic ideas of k-component order connectivity and distance-l domination, we present a quadratic-complexity algorithm that finds a tree's minimum failure-set cardinality, i.e., the minimum cardinality any subset of the tree's vertices must have so that all clusters of vertices further away than some l do not exceed a cardinality threshold. Applications of solutions to the expanded problems include choosing service center locations so that no large neighborhoods are excluded from service, while reducing the redundancy inherent in distance domination problems.