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In this paper, we propose a concept of subnet of maximum controllability based on the model of network controllability, and set up the navigation search model based on the subnet of maximum controllability, called NMSMC. The strategy of adding links that is based on the subnet of maximum controllability is to solve, with the minimum cost, the terminating search, the problem that arises from no way for particles to search in the directed network. Based on the subnet of maximum controllability to deploy navigation nodes,the search time of the whole network can be made close to the average shortest path of the navigation network,which the number of navigation nodes is only 2% of the total nodes. The experimental results of the ER and SF networks show that the search efficiency is strongly correlated with the network controllability. The better the controllability, the less the adding links are, which can lead to the fact that the more the navigation nodes are distributed in the network, the more the search efficiency of the network can be enhanced.
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Keywords:
- navigation search /
- directed network /
- network controllability
[1] Barabási A L, Albert R 2002 Rev. Mod. Phys. 74 47
[2] Newman M E J 2003 SIAM Rev. 45 167
[3] Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) [李季, 汪秉宏, 蒋品群, 周涛, 王文旭 2006 物理学报 55 4051]
[4] Feng C F, Xu X J, Wu Z X, Wang Y H 2008 Chin. Phys. B 17 1951
[5] Adamic L A, Lukose R M, Puniyani A R, Huberman B A 2001 Phys. Rev. E 64 046135
[6] Kim B J, Yoon C N, Han S K, Jeong H 2002 Phys. Rev. E 65 027103
[7] Thadakamalla H P, Albert R, Kumara S R T 2005 Phys. Rev. E 72 066128
[8] Song Q, Wang X F 2011 IEEE Trans. Intellig. Transport. Syst. 12 132
[9] Bauer R, Delling D, Sanders P, Schieferdecker D, Schultes D, Wagner D 2010 ACM J. Experiment. Algorithms 15 1
[10] Pu C L, Pei W J, Wang S P 2010 Acta Phys. Sin. 59 103 (in Chinese) [濮存来, 裴文江, 王少平 2010 物理学报 59 103]
[11] Zhou T 2008 Physica A 387 3025
[12] Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167
[13] Mller F J, Schuppert A 2011 Nature 478 E4
[14] Egerstedt M 2011 Nature 473 158
[15] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 物理学报 61 170512]
[16] Lin C T 1974 IEEE Trans. Automat. Control 19 201
[17] Wang W X, Ni X, Lai Y C, Grebogi C 2012 Phys. Rev. E 85 026115
[18] Zhou H J 2003 Phys. Rev. E 67 041908
[19] Dijkstra E W 1959 Numer. Math. 1 269
[20] Wang W X, Yin C Y, Yan G, Wang B H 2006 Phys. Rev. E 74 016101
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[1] Barabási A L, Albert R 2002 Rev. Mod. Phys. 74 47
[2] Newman M E J 2003 SIAM Rev. 45 167
[3] Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) [李季, 汪秉宏, 蒋品群, 周涛, 王文旭 2006 物理学报 55 4051]
[4] Feng C F, Xu X J, Wu Z X, Wang Y H 2008 Chin. Phys. B 17 1951
[5] Adamic L A, Lukose R M, Puniyani A R, Huberman B A 2001 Phys. Rev. E 64 046135
[6] Kim B J, Yoon C N, Han S K, Jeong H 2002 Phys. Rev. E 65 027103
[7] Thadakamalla H P, Albert R, Kumara S R T 2005 Phys. Rev. E 72 066128
[8] Song Q, Wang X F 2011 IEEE Trans. Intellig. Transport. Syst. 12 132
[9] Bauer R, Delling D, Sanders P, Schieferdecker D, Schultes D, Wagner D 2010 ACM J. Experiment. Algorithms 15 1
[10] Pu C L, Pei W J, Wang S P 2010 Acta Phys. Sin. 59 103 (in Chinese) [濮存来, 裴文江, 王少平 2010 物理学报 59 103]
[11] Zhou T 2008 Physica A 387 3025
[12] Liu Y Y, Slotine J J, Barabási A L 2011 Nature 473 167
[13] Mller F J, Schuppert A 2011 Nature 478 E4
[14] Egerstedt M 2011 Nature 473 158
[15] L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512 (in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 物理学报 61 170512]
[16] Lin C T 1974 IEEE Trans. Automat. Control 19 201
[17] Wang W X, Ni X, Lai Y C, Grebogi C 2012 Phys. Rev. E 85 026115
[18] Zhou H J 2003 Phys. Rev. E 67 041908
[19] Dijkstra E W 1959 Numer. Math. 1 269
[20] Wang W X, Yin C Y, Yan G, Wang B H 2006 Phys. Rev. E 74 016101
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