### Abstract

Robustness or fault-tolerance capability of a network is an important design parameter in both wired and wireless networks. Connectivity of a network is traditionally considered to be the primary metric for evaluation of its fault-tolerance capability. However, connectivity (G) (for random faults) or region-based connectivity _{R}(G) (for spatially correlated or region-based faults, where the faults are confined to a region R) of a network G, does not provide any information about the network state, (i.e., whether the network is connected or not) once the number of faults exceeds (G) or _{R}(G). If the number of faults exceeds (G) or _{R}(G), one would like to know, (i) the number of connected components into which G decomposes, (ii) the size of the largest connected component, (iii) the size of the smallest connected component. In this paper, we introduce a set of new metrics that computes these values. We focus on one particular metric called region-based component decomposition number (RBCDN), that measures the number of connected components in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBCDN of a network. In addition, we study the problem of least cost design of a network with a target value of RBCDN. We show that the optimal design problem is NP-complete and present an approximation algorithm with a performance bound of O(log K + 4log n), where n denotes the number of nodes in the graph and K denotes a target value of RBCDN. We evaluate the performance of our algorithm by comparing it with the performance of the optimal solution. Experimental results demonstrate that our algorithm produces near optimal solution in a fraction of time needed to find an optimal solution.

Original language | English (US) |
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Title of host publication | 2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011 |

Pages | 171-177 |

Number of pages | 7 |

DOIs | |

State | Published - 2011 |

Event | 2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011 - Cartagena, Spain Duration: Jul 4 2011 → Jul 6 2011 |

### Other

Other | 2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011 |
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Country | Spain |

City | Cartagena |

Period | 7/4/11 → 7/6/11 |

### Fingerprint

### ASJC Scopus subject areas

- Hardware and Architecture
- Electrical and Electronic Engineering

### Cite this

*2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011*(pp. 171-177). [5986022] https://doi.org/10.1109/HPSR.2011.5986022

**Beyond connectivity-new metrics to evaluate robustness of networks.** / Banerjee, Sujogya; Shirazipourazad, Shahrzad; Ghosh, Pavel; Sen, Arunabha.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011.*, 5986022, pp. 171-177, 2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011, Cartagena, Spain, 7/4/11. https://doi.org/10.1109/HPSR.2011.5986022

}

TY - GEN

T1 - Beyond connectivity-new metrics to evaluate robustness of networks

AU - Banerjee, Sujogya

AU - Shirazipourazad, Shahrzad

AU - Ghosh, Pavel

AU - Sen, Arunabha

PY - 2011

Y1 - 2011

N2 - Robustness or fault-tolerance capability of a network is an important design parameter in both wired and wireless networks. Connectivity of a network is traditionally considered to be the primary metric for evaluation of its fault-tolerance capability. However, connectivity (G) (for random faults) or region-based connectivity R(G) (for spatially correlated or region-based faults, where the faults are confined to a region R) of a network G, does not provide any information about the network state, (i.e., whether the network is connected or not) once the number of faults exceeds (G) or R(G). If the number of faults exceeds (G) or R(G), one would like to know, (i) the number of connected components into which G decomposes, (ii) the size of the largest connected component, (iii) the size of the smallest connected component. In this paper, we introduce a set of new metrics that computes these values. We focus on one particular metric called region-based component decomposition number (RBCDN), that measures the number of connected components in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBCDN of a network. In addition, we study the problem of least cost design of a network with a target value of RBCDN. We show that the optimal design problem is NP-complete and present an approximation algorithm with a performance bound of O(log K + 4log n), where n denotes the number of nodes in the graph and K denotes a target value of RBCDN. We evaluate the performance of our algorithm by comparing it with the performance of the optimal solution. Experimental results demonstrate that our algorithm produces near optimal solution in a fraction of time needed to find an optimal solution.

AB - Robustness or fault-tolerance capability of a network is an important design parameter in both wired and wireless networks. Connectivity of a network is traditionally considered to be the primary metric for evaluation of its fault-tolerance capability. However, connectivity (G) (for random faults) or region-based connectivity R(G) (for spatially correlated or region-based faults, where the faults are confined to a region R) of a network G, does not provide any information about the network state, (i.e., whether the network is connected or not) once the number of faults exceeds (G) or R(G). If the number of faults exceeds (G) or R(G), one would like to know, (i) the number of connected components into which G decomposes, (ii) the size of the largest connected component, (iii) the size of the smallest connected component. In this paper, we introduce a set of new metrics that computes these values. We focus on one particular metric called region-based component decomposition number (RBCDN), that measures the number of connected components in which the network decomposes once all the nodes of a region fail. We study the computational complexity of finding RBCDN of a network. In addition, we study the problem of least cost design of a network with a target value of RBCDN. We show that the optimal design problem is NP-complete and present an approximation algorithm with a performance bound of O(log K + 4log n), where n denotes the number of nodes in the graph and K denotes a target value of RBCDN. We evaluate the performance of our algorithm by comparing it with the performance of the optimal solution. Experimental results demonstrate that our algorithm produces near optimal solution in a fraction of time needed to find an optimal solution.

UR - http://www.scopus.com/inward/record.url?scp=80052731393&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052731393&partnerID=8YFLogxK

U2 - 10.1109/HPSR.2011.5986022

DO - 10.1109/HPSR.2011.5986022

M3 - Conference contribution

AN - SCOPUS:80052731393

SN - 9781424484560

SP - 171

EP - 177

BT - 2011 IEEE 12th International Conference on High Performance Switching and Routing, HPSR 2011

ER -