### Abstract

In this work, we consider a class of risk-averse maximum weighted subgraph problems (R-MWSP). Namely, assuming that each vertex of the graph is associated with a stochastic weight, such that the joint distribution is known, the goal is to obtain a subgraph of minimum risk satisfying a given hereditary property. We employ a stochastic programming framework that is based on the formalism of modern theory of risk measures in order to find minimum-risk hereditary structures in graphs with stochastic vertex weights. The introduced form of risk function for measuring the risk of subgraphs ensures that optimal solutions of R-MWS problems represent maximal subgraphs. A graph-based branch-and-bound (BnB) algorithm for solving the proposed problems is developed and illustrated on a special case of risk-averse maximum weighted clique problem. Numerical experiments on randomly generated Erdös-Rényi graphs demonstrate the computational performance of the developed BnB.

Original language | English (US) |
---|---|

Pages (from-to) | 167-185 |

Number of pages | 19 |

Journal | Journal of Combinatorial Optimization |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- Coherent risk measures
- Maximum weight clique problem
- Risk-averse maximum clique problem
- Risk-averse maximum weighted subgraph problem
- Stochastic weights

### ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Journal of Combinatorial Optimization*,

*28*(1), 167-185. https://doi.org/10.1007/s10878-014-9718-0

**On risk-averse maximum weighted subgraph problems.** / Rysz, Maciej; Mirghorbani, Mohammad; Krokhmal, Pavlo; Pasiliao, Eduardo L.

Research output: Contribution to journal › Article

*Journal of Combinatorial Optimization*, vol. 28, no. 1, pp. 167-185. https://doi.org/10.1007/s10878-014-9718-0

}

TY - JOUR

T1 - On risk-averse maximum weighted subgraph problems

AU - Rysz, Maciej

AU - Mirghorbani, Mohammad

AU - Krokhmal, Pavlo

AU - Pasiliao, Eduardo L.

PY - 2014/7

Y1 - 2014/7

N2 - In this work, we consider a class of risk-averse maximum weighted subgraph problems (R-MWSP). Namely, assuming that each vertex of the graph is associated with a stochastic weight, such that the joint distribution is known, the goal is to obtain a subgraph of minimum risk satisfying a given hereditary property. We employ a stochastic programming framework that is based on the formalism of modern theory of risk measures in order to find minimum-risk hereditary structures in graphs with stochastic vertex weights. The introduced form of risk function for measuring the risk of subgraphs ensures that optimal solutions of R-MWS problems represent maximal subgraphs. A graph-based branch-and-bound (BnB) algorithm for solving the proposed problems is developed and illustrated on a special case of risk-averse maximum weighted clique problem. Numerical experiments on randomly generated Erdös-Rényi graphs demonstrate the computational performance of the developed BnB.

AB - In this work, we consider a class of risk-averse maximum weighted subgraph problems (R-MWSP). Namely, assuming that each vertex of the graph is associated with a stochastic weight, such that the joint distribution is known, the goal is to obtain a subgraph of minimum risk satisfying a given hereditary property. We employ a stochastic programming framework that is based on the formalism of modern theory of risk measures in order to find minimum-risk hereditary structures in graphs with stochastic vertex weights. The introduced form of risk function for measuring the risk of subgraphs ensures that optimal solutions of R-MWS problems represent maximal subgraphs. A graph-based branch-and-bound (BnB) algorithm for solving the proposed problems is developed and illustrated on a special case of risk-averse maximum weighted clique problem. Numerical experiments on randomly generated Erdös-Rényi graphs demonstrate the computational performance of the developed BnB.

KW - Coherent risk measures

KW - Maximum weight clique problem

KW - Risk-averse maximum clique problem

KW - Risk-averse maximum weighted subgraph problem

KW - Stochastic weights

UR - http://www.scopus.com/inward/record.url?scp=84903588002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903588002&partnerID=8YFLogxK

U2 - 10.1007/s10878-014-9718-0

DO - 10.1007/s10878-014-9718-0

M3 - Article

AN - SCOPUS:84903588002

VL - 28

SP - 167

EP - 185

JO - Journal of Combinatorial Optimization

JF - Journal of Combinatorial Optimization

SN - 1382-6905

IS - 1

ER -