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Volumn 159, Issue 5, 2015, Pages 1154-1174

Statistical Mechanics of the Minimum Dominating Set Problem

Author keywords

Belief propagation; Core percolation; Dominating set; Leaf removal; Network coarse graining; Spin glass

Indexed keywords


EID: 84939973626     PISSN: 00224715     EISSN: 15729613     Source Type: Journal    
DOI: 10.1007/s10955-015-1220-2     Document Type: Article
Times cited : (52)

References (48)
  • 2
    • 84871284115 scopus 로고    scopus 로고
    • Network observability transitions
    • Yang, Y., Wang, J., Motter, A.E.: Network observability transitions. Phys. Rev. Lett. 109, 258701 (2012)
    • (2012) Phys. Rev. Lett. , vol.109 , pp. 258701
    • Yang, Y.1    Wang, J.2    Motter, A.E.3
  • 4
    • 0242509820 scopus 로고    scopus 로고
    • Statistical mechanics of the vertex-cover problem
    • Hartmann, A.K., Weigt, M.: Statistical mechanics of the vertex-cover problem. J. Phys. A 36, 11069–11093 (2003)
    • (2003) J. Phys. A , vol.36 , pp. 11069-11093
    • Hartmann, A.K.1    Weigt, M.2
  • 5
    • 84903692870 scopus 로고    scopus 로고
    • Statistical physics of hard combinatorial optimization: vertex cover problem
    • Zhao, J.-H., Zhou, H.-J.: Statistical physics of hard combinatorial optimization: vertex cover problem. Chin. Phys. B 23, 078901 (2014)
    • (2014) Chin. Phys. B , vol.23 , pp. 078901
    • Zhao, J.-H.1    Zhou, H.-J.2
  • 6
    • 37649030243 scopus 로고    scopus 로고
    • Distance-d covering problems in scale-free networks with degree correlations
    • Echenique, P., Gómez-Gardeñes, J., Moreno, Y., Vázquez, A.: Distance-$$d$$d covering problems in scale-free networks with degree correlations. Phys. Rev. E 71, 035102(R) (2005)
    • (2005) Phys. Rev. E , vol.71 , pp. 35102
    • Echenique, P.1    Gómez-Gardeñes, J.2    Moreno, Y.3    Vázquez, A.4
  • 7
    • 84904166198 scopus 로고    scopus 로고
    • Suppressing epidemics on networks by exploiting observer nodes
    • Takaguchi, T., Hasegawa, T., Yoshida, Y.: Suppressing epidemics on networks by exploiting observer nodes. Phys. Rev. E 90, 012807 (2014)
    • (2014) Phys. Rev. E , vol.90 , pp. 012807
    • Takaguchi, T.1    Hasegawa, T.2    Yoshida, Y.3
  • 8
    • 79955879494 scopus 로고    scopus 로고
    • Controllability of complex networks
    • Liu, Y.-Y., Slotine, J.-J., Barabási, A.-L.: Controllability of complex networks. Nature 473, 167–173 (2011)
    • (2011) Nature , vol.473 , pp. 167-173
    • Liu, Y.-Y.1    Slotine, J.-J.2    Barabási, A.-L.3
  • 9
    • 84900503465 scopus 로고    scopus 로고
    • Controllability in protein interaction networks
    • Wuchty, S.: Controllability in protein interaction networks. Proc. Natl. Acad. Sci. USA 111, 7156–7160 (2014)
    • (2014) Proc. Natl. Acad. Sci. USA , vol.111 , pp. 7156-7160
    • Wuchty, S.1
  • 10
    • 23044531399 scopus 로고    scopus 로고
    • A dominating-set-based routing scheme in ad hoc wireless networks
    • Wu, J., Li, H.: A dominating-set-based routing scheme in ad hoc wireless networks. Telecomm. Syst. 18, 13–36 (2001)
    • (2001) Telecomm. Syst. , vol.18 , pp. 13-36
    • Wu, J.1    Li, H.2
  • 13
    • 0028514351 scopus 로고
    • On the hardness of approximating minimization problems
    • Lund, C., Yannakakis, M.: On the hardness of approximating minimization problems. J. ACM 41, 960–981 (1994)
    • (1994) J. ACM , vol.41 , pp. 960-981
    • Lund, C.1    Yannakakis, M.2
  • 14
    • 85203765783 scopus 로고    scopus 로고
    • Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability pcp characterization of np. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 475–484 (ACM, New York, 1997)
    • Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability pcp characterization of np. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 475–484 (ACM, New York, 1997)
  • 15
    • 84861525639 scopus 로고    scopus 로고
    • Simulated annealing with stochastic local search for minimum dominating set problem
    • Hedar, A.-R., Ismail, R.: Simulated annealing with stochastic local search for minimum dominating set problem. Int. J. Mach. Learn. Cybernet. 3, 97–109 (2012)
    • (2012) Int. J. Mach. Learn. Cybernet. , vol.3 , pp. 97-109
    • Hedar, A.-R.1    Ismail, R.2
  • 17
    • 0001327869 scopus 로고    scopus 로고
    • Core percolation in random graphs: a critical phenomena analysis
    • Bauer, M., Golinelli, O.: Core percolation in random graphs: a critical phenomena analysis. Eur. Phys. J. B 24, 339–352 (2001)
    • (2001) Eur. Phys. J. B , vol.24 , pp. 339-352
    • Bauer, M.1    Golinelli, O.2
  • 18
    • 84903628832 scopus 로고    scopus 로고
    • The statistical mechanics of random set packing and a generalization of the Karp–Sipser algorithm
    • Lucibello, C., Ricci-Tersenghi, F.: The statistical mechanics of random set packing and a generalization of the Karp–Sipser algorithm. Int. J. Stat. Mech. 2014, 136829 (2014)
    • (2014) Int. J. Stat. Mech. , vol.2014 , pp. 136829
    • Lucibello, C.1    Ricci-Tersenghi, F.2
  • 19
    • 84903639148 scopus 로고    scopus 로고
    • Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm
    • Takabe, S., Hukushima, K.: Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm. Phys. Rev. E 89, 062139 (2014)
    • (2014) Phys. Rev. E , vol.89 , pp. 062139
    • Takabe, S.1    Hukushima, K.2
  • 21
    • 0036013593 scopus 로고    scopus 로고
    • Statistical mechanics of complex networks
    • Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
    • (2002) Rev. Mod. Phys. , vol.74 , pp. 47-97
    • Albert, R.1    Barabási, A.-L.2
  • 22
    • 0035981014 scopus 로고    scopus 로고
    • Universal behavior of load distribution in scale-free networks
    • Goh, K.-I., Kahng, B., Kim, D.: Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87, 278701 (2001)
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 278701
    • Goh, K.-I.1    Kahng, B.2    Kim, D.3
  • 23
    • 84891366575 scopus 로고    scopus 로고
    • Inducing effect on the percolation transition in complex networks
    • Zhao, J.-H., Zhou, H.-J., Liu, Y.-Y.: Inducing effect on the percolation transition in complex networks. Nat. Commun. 4, 2412 (2013)
    • (2013) Nat. Commun. , vol.4 , pp. 2412
    • Zhao, J.-H.1    Zhou, H.-J.2    Liu, Y.-Y.3
  • 24
    • 21244448624 scopus 로고    scopus 로고
    • Long-range frustration in a spin-glass model of the vertex-cover problem
    • Zhou, H.J.: Long-range frustration in a spin-glass model of the vertex-cover problem. Phys. Rev. Lett. 94, 217203 (2005)
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 217203
    • Zhou, H.J.1
  • 25
    • 84869072547 scopus 로고    scopus 로고
    • Erratum: long-range frustration in a spin-glass model of the vertex-cover problem [phys. rev. lett. 94, 217203 (2005)]
    • Zhou, H.-J.: Erratum: long-range frustration in a spin-glass model of the vertex-cover problem [phys. rev. lett. 94, 217203 (2005)]. Phys. Rev. Lett. 109, 199901 (2012)
    • (2012) Phys. Rev. Lett. , vol.109 , pp. 199901
    • Zhou, H.-J.1
  • 26
    • 17744376167 scopus 로고    scopus 로고
    • Analytic solution of a static scale-free network model
    • Catanzaro, M., Pastor-Satorras, R.: Analytic solution of a static scale-free network model. Eur. Phys. J. B 44, 241–248 (2005)
    • (2005) Eur. Phys. J. B , vol.44 , pp. 241-248
    • Catanzaro, M.1    Pastor-Satorras, R.2
  • 27
    • 22544449853 scopus 로고    scopus 로고
    • Dynamic pattern evolution on scale-free networks
    • Zhou, H.J., Lipowsky, R.: Dynamic pattern evolution on scale-free networks. Proc. Natl. Acad. Sci. USA 102, 10052–10057 (2005)
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 10052-10057
    • Zhou, H.J.1    Lipowsky, R.2
  • 28
    • 79960066197 scopus 로고    scopus 로고
    • Robust network community detection using balanced propagation
    • Šubelj, L., Bajec, M.: Robust network community detection using balanced propagation. Eur. Phys. J. B 81, 353–362 (2011)
    • (2011) Eur. Phys. J. B , vol.81 , pp. 353-362
    • Šubelj, L.1    Bajec, M.2
  • 29
    • 84924178998 scopus 로고    scopus 로고
    • Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters
    • Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters. Internet Math. 6, 29–123 (2009)
    • (2009) Internet Math. , vol.6 , pp. 29-123
    • Leskovec, J.1    Lang, K.J.2    Dasgupta, A.3    Mahoney, M.W.4
  • 30
    • 0032482432 scopus 로고    scopus 로고
    • Collective dynamics of ’small-world’ netowrks
    • Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ netowrks. Nature 393, 440–442 (1998)
    • (1998) Nature , vol.393 , pp. 440-442
    • Watts, D.J.1    Strogatz, S.H.2
  • 33
    • 0036187056 scopus 로고    scopus 로고
    • Mapping the gnutella network: properties of large-scale peer-to-peer systems and implications for system design
    • Ripeanu, M., Foster, I., Iamnitchi, A.: Mapping the gnutella network: properties of large-scale peer-to-peer systems and implications for system design. IEEE Internet Comput. 6, 50–57 (2002)
    • (2002) IEEE Internet Comput. , vol.6 , pp. 50-57
    • Ripeanu, M.1    Foster, I.2    Iamnitchi, A.3
  • 35
    • 0038074373 scopus 로고    scopus 로고
    • Topological structure analysis of the protein–protein interaction network in budding yeast
    • Bu, D., et al.: Topological structure analysis of the protein–protein interaction network in budding yeast. Nucleic Acids Res. 31, 2443–2450 (2003)
    • (2003) Nucleic Acids Res. , vol.31 , pp. 2443-2450
    • Bu, D.1
  • 37
    • 80053607947 scopus 로고    scopus 로고
    • Partition function loop series for a general graphical model: free-energy corrections and message-passing equations
    • Xiao, J.-Q., Zhou, H.J.: Partition function loop series for a general graphical model: free-energy corrections and message-passing equations. J. Phys. A 44, 425001 (2011)
    • (2011) J. Phys. A , vol.44 , pp. 425001
    • Xiao, J.-Q.1    Zhou, H.J.2
  • 38
    • 84865423021 scopus 로고    scopus 로고
    • Region graph partition function expansion and approximate free energy landscapes: theory and some numerical results
    • Zhou, H.J., Wang, C.: Region graph partition function expansion and approximate free energy landscapes: theory and some numerical results. J. Stat. Phys. 148, 513–547 (2012)
    • (2012) J. Stat. Phys. , vol.148 , pp. 513-547
    • Zhou, H.J.1    Wang, C.2
  • 39
    • 0037008520 scopus 로고    scopus 로고
    • Analytic and algorithmic solution of random satisfiability problems
    • Mézard, M., Parisi, G., Zecchina, R.: Analytic and algorithmic solution of random satisfiability problems. Science 297, 812–815 (2002)
    • (2002) Science , vol.297 , pp. 812-815
    • Mézard, M.1    Parisi, G.2    Zecchina, R.3
  • 42
    • 84885091186 scopus 로고    scopus 로고
    • Optimizing spread dynamics on graphs by message passing. J. Stat
    • Altarelli, F., Braunstein, A., Dall’Asta, L., Zecchina, R.: Optimizing spread dynamics on graphs by message passing. J. Stat. Mech. (2013). doi:10.1088/1742-5468/2013/09/P09011
    • (2013) Mech
    • Altarelli, F.1    Braunstein, A.2    Dall’Asta, L.3    Zecchina, R.4
  • 43
    • 84908148509 scopus 로고    scopus 로고
    • Minimal contagious sets in random regular graphs
    • Guggiola, A., Semerjian, G.: Minimal contagious sets in random regular graphs. J. Stat. Phys. 158, 300–358 (2015)
    • (2015) J. Stat. Phys. , vol.158 , pp. 300-358
    • Guggiola, A.1    Semerjian, G.2
  • 44
    • 84886032458 scopus 로고    scopus 로고
    • Observability transitions in correlated networks
    • Hasegawa, T., Takaguchi, T., Masuda, N.: Observability transitions in correlated networks. Phys. Rev. E 88, 042809 (2013)
    • (2013) Phys. Rev. E , vol.88 , pp. 042809
    • Hasegawa, T.1    Takaguchi, T.2    Masuda, N.3
  • 45
    • 0038401954 scopus 로고    scopus 로고
    • The bethe lattice spin glass revisited
    • Mézard, M., Parisi, G.: The bethe lattice spin glass revisited. Eur. Phys. J. B 20, 217–233 (2001)
    • (2001) Eur. Phys. J. B , vol.20 , pp. 217-233
    • Mézard, M.1    Parisi, G.2
  • 46
    • 33750071082 scopus 로고    scopus 로고
    • Reconstruction on trees and spin glass transition
    • Mézard, M., Montanari, A.: Reconstruction on trees and spin glass transition. J. Stat. Phys. 124, 1317–1350 (2006)
    • (2006) J. Stat. Phys. , vol.124 , pp. 1317-1350
    • Mézard, M.1    Montanari, A.2
  • 47
    • 85203756590 scopus 로고    scopus 로고
    • Habibulla, Y., Zhao, J.-H., Zhou, H.-J.: The directed dominating set problem: generalized leaf removal and belief propagation. (2015, in preparation)
    • Habibulla, Y., Zhao, J.-H., Zhou, H.-J.: The directed dominating set problem: generalized leaf removal and belief propagation. (2015, in preparation)


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