Heuristics for Synthesizing Robust Networks with a Diameter Constraint

Robustness of a network in the presence of node or link failures plays an important role in the design of the network. A key factor that quantifies this robustness is the algebraic connectivity of the network. In this paper, the authors address the problem of finding a network that maximizes the algebraic connectivity of the network while ensuring that the length of the shortest path joining any two nodes in the network is within a given bound. This paper presents -opt and tabu search heuristics for finding feasible solutions for this network synthesis problem. Computational results are also presented to corroborate the performance of the proposed algorithms.

[1]  Bruce J. Holmes,et al.  Transportation Network Topologies , 2004 .

[2]  Rex K. Kincaid,et al.  An investigation of synchrony in transport networks , 2009, Complex..

[3]  Harsha Nagarajan,et al.  Algorithms for Finding Diameter-constrained Graphs with Maximum Algebraic Connectivity , 2012 .

[4]  Joseph Post,et al.  Impact of Commercial Airline Network Evolution on the U.S. Air Transportation System , 2011 .

[5]  Raymond H. Byrne,et al.  Algebraic connectivity and graph robustness. , 2009 .

[6]  Harsha Nagarajan,et al.  Algorithms for synthesizing mechanical systems with maximal natural frequencies , 2012 .

[7]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[8]  G. Croes.  A Method for Solving Traveling-Salesman Problems , 1958 .

[9]  Rex K. Kincaid,et al.  An investigation of synchrony in transport networks , 2009 .

[10]  Rex K. Kincaid,et al.  Toward Optimal Transport Networks , 2008 .

[11]  Stephen P. Boyd,et al.  Growing Well-connected Graphs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[12]  Peng Wei,et al.  Weighted Algebraic Connectivity: An Application to Airport Transportation Network , 2011 .

[13]  Piet Van Mieghem,et al.  On the Robustness of Complex Networks by Using the Algebraic Connectivity , 2008, Networking.

[14]  Damon Mosk-Aoyama,et al.  Maximum algebraic connectivity augmentation is NP-hard , 2008, Operations Research Letters.

[15]  S. Conway.  Scale-Free Networks and Commercial Air Carrier Transportation in the United States , 2004 .

[16]  Roger Guimerà,et al.  Modeling the world-wide airport network , 2004 .

[17]  A. Jamakovic,et al.  On the relationship between the algebraic connectivity and graph's robustness to node and link failures , 2007, 2007 Next Generation Internet Networks.