# Graph Fragmentation Problem

### Juan Piccini, Franco Robledo, Pablo Romero

#### Abstract

A combinatorial optimization problem called Graph Fragmentation Problem (GFP) is introduced. The decision variable is a set of protected nodes, which are deleted from the graph. An attacker picks a non-protected node uniformly at random from the resulting subgraph, and it completely affects the corresponding connected component. The goal is to minimize the expected number of affected nodes S. The GFP finds applications in fire fighting, epidemiology and robust network design among others. A Greedy notion for the GFP is presented. Then, we develop a GRASP heuristic enriched with a Path-Relinking post-optimization phase. Both heuristics are compared on the lights of graphs inspired by a real-world application.

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#### Paper Citation

#### in Harvard Style

Piccini J., Robledo F. and Romero P. (2016). **Graph Fragmentation Problem** . In *Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-171-7, pages 137-144. DOI: 10.5220/0005697701370144

#### in Bibtex Style

@conference{icores16,

author={Juan Piccini and Franco Robledo and Pablo Romero},

title={Graph Fragmentation Problem},

booktitle={Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2016},

pages={137-144},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005697701370144},

isbn={978-989-758-171-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of 5th the International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Graph Fragmentation Problem

SN - 978-989-758-171-7

AU - Piccini J.

AU - Robledo F.

AU - Romero P.

PY - 2016

SP - 137

EP - 144

DO - 10.5220/0005697701370144