The parameterized complexity of finding secluded solutions to some classical optimization problems on graphs

TL;DR

This paper investigates the parameterized complexity of finding solutions in graphs that are not only optimal but also have minimal neighborhoods, with applications in secure routing and community detection.

Contribution

It introduces the complexity analysis of secluded solutions for classical graph problems, extending understanding of their computational difficulty.

Findings

Provides complexity classifications for secluded solutions

Identifies fixed-parameter tractability in certain cases

Highlights applications in security and community detection

Abstract

This work studies the parameterized complexity of finding secluded solutions to classical combinatorial optimization problems on graphs such as finding minimum s-t separators, feedback vertex sets, dominating sets, maximum independent sets, and vertex deletion problems for hereditary graph properties: Herein, one searches not only to minimize or maximize the size of the solution, but also to minimize the size of its neighborhood. This restriction has applications in secure routing and community detection.