Abstract
This paper introduces six new failure-independent multi-path computation problems in complex networks such as smart grid communication network, each of which comes with unique failure interdependency assumptions. Despite the difference of the formulation of the problems, we show that each of the problems can be reduced to another within polynomial time, and therefore they are equivalent in terms of hardness. Then, we show that they are not only \(\mathcal {NP}\)-hard, but also cannot be approximated within a certain bound unless \(\mathcal {P}=\mathcal {NP}\). Besides, we show that their decision problem versions to determine if there exist two failure independent paths between two given end nodes are still \(\mathcal {NP}\)-complete. As a result, this paper opens a new series of research problems with daunting complexity based on important real world applications.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
United States Department of Energy. Smart Grid/Department of Energy. Accessed 18 June 2012
Ishida, K., Kakuda, Y., Kikuno, T.: A routing protocol for finding two node-disjoint paths in computer networks. In: Proceedings of International Conference on Network Protocols (ICNP), pp. 340–347 (1992)
Nikolopoulos, S.D., Pitsillides, A., Tipper, D.: Addressing network survivability issues by finding the \(K\)-best paths through a trellis graph. In: Proceedings of the 16th IEEE International Conference on Computer Communications (INFOCOM) (1997)
Wang, J., Yang, M., Qi, X., Cook, R.: Dual-homing multicast protection. In: Proceedings of IEEE Global Telecommunications Conference (GLOBECOM), pp. 1123–1127 (2004)
Wang, J., Yang, M., Yang, B., Zheng, S.Q.: Dual-homing based scalable partial multicast protection. IEEE Trans. Comput. (TC) 55(9), 1130–1141 (2006)
Yang, B., Zheng, S.Q., Katukam, S.: Finding two disjoint paths in a network with min-min objective function. In: Proceedings of the 15th IASTED International Conference on Parallel and Distributed Computing and Systems, pp. 75–80 (2003)
Yang, B., Zheng, S.Q., Lu, E.: Finding two disjoint paths in a network with normalized \(\mathit{\alpha }^{+}\)-MIN-SUM objective function. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 954–963. Springer, Heidelberg (2005). https://doi.org/10.1007/11602613_95
Yang, B., Zheng, S.Q., Lu, E.: Finding two disjoint paths in a network with normalized \(\alpha ^-\)-MIN-SUM objective function. In: Proceeding of the 17th International Conference on Parallel and Distributed Computing Systems (PDCS) (2005)
Yang, B., Zheng, S.Q., Lu, E.: Finding two disjoint paths in a network with minsum-minmin objective function. In: Proceedings of the 2007 International Conference on Foundations of Computer Science (FCS) (2007)
Yang, M., Wang, J., Qi, X., Jiang, Y.: On finding the best partial multicast protection tree under dual-homing architecture. In: Proceedings of the Workshop on High Performance Switching and Routing (HPSR) (2005)
Chen, X., Dinh, H., Wang, B.: Cascading failures in smart grid - benefits of distributed generation. In: Proceedings of the 1st International Conference Smart Grid Communications (SmartGridComm) (2010)
Ruj, S., Pal, A.: Analyzing cascading failures in smart grids under random and targeted attacks. In: Proceedings of the 28th IEEE International Conference on Advanced Information Networking and Applications (AINA) (2014)
Huang, Z., Wang, C., Stojmenovic, M., Nayak, A.: Balancing system survivability and cost of smart grid via modeling cascading failures. IEEE Trans. Emerg. Topics Comput. (TETC) 1(1), 45–56 (2013)
Nguyen, D.T., Shen, Y., Thai, M.T.: Detecting critical nodes in interdependent power networks for vulnerability assessment. IEEE Trans. Smart Grid (TSG) 4(1), 151–159 (2013)
Hayashi, M., Abe, T.: Network Reliability. IEICE, Tokyo (2010). (in Japanese)
Grubesic, T.H., O’Kelly, M.E., Murray, A.T.: A geographic perspective on commercial internet survivability. Telematics Inform. 20, 51–69 (2003)
Liew, S.C., Lu, K.W.: A framework for characterizing disaster-based network survivability. IEEE J. Sel. Areas Commun. (JSAC) 12(1), 52–58 (1994)
Bienstock, D.: Some generalized max-flow min-cut problems in the plane. Math. Meth. Oper. Res. 16(2), 310–333 (1991)
Wu, W., Moran, B., Manton, J., Zukerman, M.: Topology design of undersea cables considering survivability under major disasters. In: Proceedings of the IEEE 23rd International Conference on Advanced Information Networking and Applications (WAINA) (2009)
Sen, A., Shen, B.H., Zhou, L., Hao, B.: Fault-tolerance in sensor networks: a new evaluation metric. In: Proceedings of the 25th IEEE International Conference on Computer Communications (INFOCOM) (2006)
Neumayer, S., Efrat, A., Modiano, E.: Geographic max-flow and min-cut under a circular disk failure model. In: Proceedings of the 31st IEEE International Conference on Computer Communications (INFOCOM) (2012)
Zhang, X., Perrig, A.: Correlation-resilient path selection in multi-path routing. In: Proceedings of IEEE Global Telecommunications Conference (GLOBECOM) (2010)
Hong, Y., Kim, D., Li, D., Guo, L., Son, J., Tokuta, A.O.: Two new multi-path routing algorithms for fault-tolerant communications in smart grid. Ad Hoc Netw. (ADHOC) 22, 3–12 (2014)
Godsil, C., Royle, G.: Algebraic Graph Theory. Springer, New York (2001)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Zuckerman, D.: Linear degree extractors and the inapproximability of max clique and chromatic number. In: Proceedings of 38th ACM Symposium on Theory of Computing, pp. 681–690 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Yang, Z., Kim, D., Wang, W. (2017). On Interdependent Failure Resilient Multi-path Routing in Smart Grid Communication Network. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-71147-8_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-71146-1
Online ISBN: 978-3-319-71147-8
eBook Packages: Computer ScienceComputer Science (R0)