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Dangerous Graphs

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Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

Anomalies and faults are inevitable in computer networks, today more than ever before. This is due to the large scale and dynamic nature of the networks used to process big data and to the ever-increasing number of ad-hoc devices. Beyond natural faults and anomalies occurring in a network, threats proceeding from attacks conducted by malicious intruders must be considered. Consequently, there is often a need to quickly isolate and even repair a fault in a network when it appears. Furthermore, despite the presence in a network of faults stemming from malicious entities, we need to identify the latter and their behaviours, and develop protocols resilient to their attacks. Thus, defining models to capture the dangers inherent to various faults, anomalies and threats in a network and studying such threats, has become increasingly important and popular.

Threats in networks can be of two kinds: either mobile or stationary. A malicious mobile process can move along the network, whereas a stationary harmful process resides in a host. One of the most studied models for stationary harmful processes is the black hole, which was introduced by Dobrev, Flocchini, Prencipe and Santoro in 2001. A black hole models a network node in which a destructive process deletes any visiting agent or incoming data upon arrival, without leaving any observable trace. Conversely, a network may face one or more malicious mobile processes infecting one or more nodes. Given both kinds of threats, a first crucial task consists in searching for and reporting as quickly as possible the location all faulty nodes while using a minimum number of mobile agents. In general, the main issue is to identify the minimal hypotheses under which faulty nodes can be found. This problem has been investigated in both asynchronous and synchronous networks. A corollary task is to make sure that the protocols designed for solving problems such as gathering and transferring data still work despite the presence of one or more faulty nodes.

In this chapter, we review the state-of-the-art of research pertaining to the presence of faulty nodes in a network. We discuss different models in synchronous and asynchronous networks and for different communication and computation capabilities of the agents. We also address relevant computational issues and present algorithmic techniques and impossibility results.

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Notes

  1. 1.

    Given the old result of Rollik in [100] (discussed in the beginning of the section) which proved that no finite set of finite automata can cooperatively perform exploration of all cubic planar graphs.

  2. 2.

    An open vertex cover by cycles (C) is defined as a set of simple cycles such that (a) each vertex of G is covered by a cycle from C and (b) the connectivity graph of these cycles (where each cycle is represented by a vertex, and 2 vertices are connected if the corresponding cycles share an edge) is connected.

References

  1. Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput. 36(1), 56–82 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Agrawal, P., Ghosh, R.K., Das, S.K.: Cooperative black and gray hole attacks in mobile ad hoc networks. In: Proceedings of the 2nd International Conference on Ubiquitous Information Management and Communication, ICUIMC 2008, pp. 310–314. ACM, New York (2008)

    Google Scholar 

  3. Al-Shurman, M., Yoo, S.-M., Park, S.: Black hole attack in mobile ad hoc networks. In: Proceedings of the 42nd Annual Southeast Regional Conference, pp. 96–97. ACM (2004)

    Google Scholar 

  4. Albers, S., Henzinger, M.R.: Exploring unknown environments. SIAM J. Comput. 29(4), 1164–1188 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Asaka, M., Okazawa, S., Taguchi, A., Goto, S.: A method of tracing intruders by use of mobile agents. In: Proceedings of of 9th Annual Conference of the Internet Society (1999). http://www.isoc.org/

  6. Balamohan, B., Dobrev, S., Flocchini, P., Santoro, N.: Asynchronous exploration of an unknown anonymous dangerous graph with O(1) pebbles. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 279–290. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31104-8_24

    Chapter  Google Scholar 

  7. Balamohan, B., Flocchini, P., Miri, A., Santoro, N.: Improving the optimal bounds for black hole search in rings. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 198–209. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22212-2_18

    Chapter  Google Scholar 

  8. Balamohan, B., Flocchini, P., Miri, A., Santoro, N.: Time optimal algorithms for black hole search in rings. Discret. Math. Algorithms Appl. 3(4), 457–471 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bampas, E., Leonardos, N., Markou, E., Pagourtzis, A., Petrolia, M.: Improved periodic data retrieval in asynchronous rings with a faulty host. Theor. Comput. Sci. 608, 231–254 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Banerjee, S.: Detection/removal of cooperative black and gray hole attack in mobile ad-hoc networks. In: Proceedings of the World Congress on Engineering and Computer Science, pp. 22–24 (2008)

    Google Scholar 

  11. Banerjee, S., Sardar, M., Majumder, K.: AODV based black-hole attack mitigation in MANET. In: Satapathy, S., Udgata, S., Biswal, B. (eds.) FICTA 2013. AISC, vol. 247, pp. 345–352. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-02931-3_39

    Chapter  Google Scholar 

  12. Barriere, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Capture of an intruder by mobile agents. In: Proceedings of 14th ACM Symposium on Parallel Algorithms and Architectures, pp. 200–209 (2002)

    Google Scholar 

  13. Bender, M.A., Fernández, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: exploring and mapping directed graphs. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 269–278. ACM (1998)

    Google Scholar 

  14. Bender, M.A., Slonim, D.: The power of team exploration: two robots can learn unlabeled directed graphs. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science, pp. 75–85 (1994)

    Google Scholar 

  15. Blin, L., Fraigniaud, P., Nisse, N., Vial, S.: Distributed chasing of network intruders. In: Flocchini, P., Gąsieniec, L. (eds.) SIROCCO 2006. LNCS, vol. 4056, pp. 70–84. Springer, Heidelberg (2006). https://doi.org/10.1007/11780823_7

    Chapter  Google Scholar 

  16. Borselius, N.: Mobile agent security. Electron. Commun. Eng. J. 14(5), 211–218 (2002)

    Article  Google Scholar 

  17. Cai, J., Flocchini, P., Santoro, N.: Network decontamination from a black virus. In: 2013 IEEE 27th International Parallel and Distributed Processing Symposium Workshops & Ph.D. Forum (IPDPSW), pp. 696–705. IEEE (2013)

    Google Scholar 

  18. Cai, J., Flocchini, P., Santoro, N.: Decontaminating a network from a black virus. Int. J. Netw. Comput. 4(1), 151–173 (2014)

    Article  Google Scholar 

  19. Cai, J., Flocchini, P., Santoro, N.: Distributed black virus decontamination and rooted acyclic orientations. In: 2015 IEEE International Conference on Computer and Information Technology; Ubiquitous Computing and Communications; Dependable, Autonomic and Secure Computing; Pervasive Intelligence and Computing (CIT/IUCC/DASC/PICOM), pp. 1681–1688. IEEE (2015)

    Google Scholar 

  20. Chalopin, J., Das, S., Labourel, A., Markou, E.: Black hole search with finite automata scattered in a synchronous torus. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 432–446. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24100-0_41

    Chapter  Google Scholar 

  21. Chalopin, J., Das, S., Labourel, A., Markou, E.: Tight bounds for scattered black hole search in a ring. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 186–197. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22212-2_17

    Chapter  Google Scholar 

  22. Chalopin, J., Das, S., Labourel, A., Markou, E.: Tight bounds for black hole search with scattered agents in synchronous rings. Theor. Comput. Sci. (TCS) 509, 70–85 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chalopin, J., Das, S., Santoro, N.: Rendezvous of mobile agents in unknown graphs with faulty links. In: Proceedings of 21st International Conference on Distributed Computing, pp. 108–122 (2007)

    Google Scholar 

  24. Chess, D.M.: Security issues in mobile code systems. In: Vigna, G. (ed.) Mobile Agents and Security. LNCS, vol. 1419, pp. 1–14. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-68671-1_1

    Chapter  Google Scholar 

  25. Cooper, C., Klasing, R., Radzik, T.: Searching for black-hole faults in a network using multiple agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 320–332. Springer, Heidelberg (2006). https://doi.org/10.1007/11945529_23

    Chapter  Google Scholar 

  26. Cooper, C., Klasing, R., Radzik, T.: Locating and repairing faults in a network with mobile agents. Theor. Comput. Sci. 411(14–15), 1638–1647 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Czyzowicz, J., et al.: More efficient periodic traversal in anonymous undirected graphs. Theor. Comput. Sci. 444, 60–76 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Czyzowicz, J., Dobrev, S., Kralovic, R., Miklik, S., Pardubska, D.: Black hole search in directed graphs. In: Proceedings of 16th International Colloquium on Structural Information and Communication Complexity, pp. 182–194 (2009)

    Chapter  Google Scholar 

  29. Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Searching for a black hole in tree networks. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 67–80. Springer, Heidelberg (2005). https://doi.org/10.1007/11516798_5

    Chapter  Google Scholar 

  30. Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Complexity of searching for a black hole. Fundamenta Informaticae 71(2,3), 229–242 (2006)

    MathSciNet  MATH  Google Scholar 

  31. Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Searching for a black hole in synchronous tree networks. Comb. Probab. Comput. 16(4), 595–619 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Das, S., Flocchini, P., Kutten, S., Nayak, A., Santoro, N.: Map construction of unknown graphs by multiple agents. Theor. Comput. Sci. 385(1–3), 34–48 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  33. Das, S., Focardi, R., Luccio, F., Markou, E., Squarcina, M.: Gathering of robots in a ring with mobile faults. Theor. Comput. Sci. (2018, to appear)

    Google Scholar 

  34. Das, S., Luccio, F.L., Markou, E.: Mobile agents rendezvous in spite of a malicious agent. In: Bose, P., Gąsieniec, L.A., Römer, K., Wattenhofer, R. (eds.) ALGOSENSORS 2015. LNCS, vol. 9536, pp. 211–224. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-28472-9_16

    Chapter  Google Scholar 

  35. D’Emidio, M., Frigioni, D., Navarra, A.: Exploring and making safe dangerous networks using mobile entities. In: Cichoń, J., Gȩbala, M., Klonowski, M. (eds.) ADHOC-NOW 2013. LNCS, vol. 7960, pp. 136–147. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39247-4_12

    Chapter  Google Scholar 

  36. D’Emidio, M., Frigioni, D., Navarra, A.: Explore and repair graphs with black holes using mobile entities. Theor. Comput. Sci. 605, 129–145 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  37. Deng, X., Kameda, T., Papadimitriou, C.H.: How to learn an unknown environment I: the rectilinear case. J. ACM 45, 215–245 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  38. Diks, K., Fraigniaud, P., Kranakis, E., Pelc, A.: Tree exploration with little memory. J. Algorithms 51, 38–63 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. Dobrev, S., Flocchini, P., Královič, R., Prencipe, G., Ruzicka, P., Santoro, N.: Black hole search by mobile agents in hypercubes and related networks. In: OPODIS, vol. 3, pp. 169–180 (2002)

    Google Scholar 

  40. Dobrev, S., Flocchini, P., Královič, R., Ružička, P., Prencipe, G., Santoro, N.: Black hole search in common interconnection networks. Networks 47(2), 61–71 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  41. Dobrev, S., Flocchini, P., Královič, R., Santoro, N.: Exploring an unknown graph to locate a black hole using tokens. In: Navarro, G., Bertossi, L., Kohayakawa, Y. (eds.) TCS 2006. IIFIP, vol. 209, pp. 131–150. Springer, Boston, MA (2006). https://doi.org/10.1007/978-0-387-34735-6_14

    Chapter  Google Scholar 

  42. Dobrev, S., Flocchini, P., Královič, R., Santoro, N.: Exploring an unknown dangerous graph using tokens. Theor. Comput. Sci. 472, 28–45 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  43. Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Mobile search for a black hole in an anonymous ring. In: Welch, J. (ed.) DISC 2001. LNCS, vol. 2180, pp. 166–179. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45414-4_12

    Chapter  Google Scholar 

  44. Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: optimal mobile agent protocols. In: Proceedings of the Twenty-first Annual Symposium on Principles of Distributed Computing, PODC 2002, pp. 153–162. ACM, New York (2002)

    Google Scholar 

  45. Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Multiple agents rendezvous in a ring in spite of a black hole. In: Papatriantafilou, M., Hunel, P. (eds.) OPODIS 2003. LNCS, vol. 3144, pp. 34–46. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27860-3_6

    Chapter  MATH  Google Scholar 

  46. Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: optimal mobile agents protocols. Distrib. Comput. 19(1), 1–18 (2006)

    Article  MATH  Google Scholar 

  47. Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Mobile search for a black hole in an anonymous ring. Algorithmica 48, 67–90 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  48. Dobrev, S., Flocchini, P., Santoro, N.: Improved bounds for optimal black hole search with a network map. In: Královic̆, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 111–122. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27796-5_11

    Chapter  Google Scholar 

  49. Dobrev, S., Flocchini, P., Santoro, N.: Cycling through a dangerous network: a simple efficient strategy for black hole search. In: Proceedings of the 26th IEEE International Conference on Distributed Computing Systems, ICDCS 2006, p. 57. IEEE Computer Society, Washington, DC (2006)

    Google Scholar 

  50. Dobrev, S., Královič, R., Santoro, N., Shi, W.: Black hole search in asynchronous rings using tokens. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds.) CIAC 2006. LNCS, vol. 3998, pp. 139–150. Springer, Heidelberg (2006). https://doi.org/10.1007/11758471_16

    Chapter  Google Scholar 

  51. Dobrev, S., Santoro, N., Shi, W.: Locating a black hole in an un-oriented ring using tokens: the case of scattered agents. In: Kermarrec, A.-M., Bougé, L., Priol, T. (eds.) Euro-Par 2007. LNCS, vol. 4641, pp. 608–617. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74466-5_64

    Chapter  Google Scholar 

  52. Dobrev, S., Santoro, N., Shi, W.: Scattered black hole search in an oriented ring using tokens. In: Proceedings of IEEE International Parallel and Distributed Processing Symposium, pp. 1–8 (2007)

    Google Scholar 

  53. Dobrev, S., Santoro, N., Shi, W.: Using scattered mobile agents to locate a black hole in an un-oriented ring with tokens. Int. J. Found. Comput. Sci. 19(6), 1355–1372 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  54. Duncan, C.A., Kobourov, S.G., Kumar, V.S.: Optimal constrained graph exploration. In: Proceedings of 12th Annual ACM Symposium on Discrete Algorithms, pp. 807–814 (2001)

    Google Scholar 

  55. Engebretsen, L., Karpinski, M.: TSP with bounded metrics. J. Comput. Syst. Sci. 72(4), 509–546 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  56. Flocchini, P., Huang, M.J., Luccio, F.L.: Contiguous search in the hypercube for capturing an intruder. In: Proceedings of 18th IEEE International Parallel and Distributed Processing Symposium (2005)

    Google Scholar 

  57. Flocchini, P., Huang, M.J., Luccio, F.L.: Decontamination of chordal rings and tori. In: Proceedings of 8th Workshop on Advances in Parallel and Distributed Computational Models (2006)

    Google Scholar 

  58. Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: ring exploration by asynchronous oblivious robots. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 105–118. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-77096-1_8

    Chapter  Google Scholar 

  59. Flocchini, P., Ilcinkas, D., Santoro, N.: Ping pong in dangerous graphs: optimal black hole search with pure tokens. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 227–241. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87779-0_16

    Chapter  Google Scholar 

  60. Flocchini, P., Ilcinkas, D., Santoro, N.: Ping pong in dangerous graphs: optimal black hole search with pebbles. Algorithmica 62(3–4), 1006–1033 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  61. Flocchini, P., Kellett, M., Mason, P., Santoro, N.: Map construction and exploration by mobile agents scattered in a dangerous network. In: Proceedings of IEEE International Symposium on Parallel & Distributed Processing, pp. 1–10 (2009)

    Google Scholar 

  62. Flocchini, P., Kellett, M., Mason, P., Santoro, N.: Searching for black holes in subways. Theory Comput. Syst. 50(1), 158–184 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  63. Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Mapping an unfriendly subway system. In: Boldi, P., Gargano, L. (eds.) FUN 2010. LNCS, vol. 6099, pp. 190–201. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13122-6_20

    Chapter  Google Scholar 

  64. Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Fault-tolerant exploration of an unknown dangerous graph by scattered agents. In: Richa, A.W., Scheideler, C. (eds.) SSS 2012. LNCS, vol. 7596, pp. 299–313. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33536-5_30

    Chapter  Google Scholar 

  65. Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Finding good coffee in Paris. In: Kranakis, E., Krizanc, D., Luccio, F. (eds.) FUN 2012. LNCS, vol. 7288, pp. 154–165. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30347-0_17

    Chapter  Google Scholar 

  66. Flocchini, P., Luccio, F.L., Song, L.X.: Size optimal strategies for capturing an intruder in mesh networks. In: Communications in Computing, pp. 200–206 (2005)

    Google Scholar 

  67. Flocchini, P., Mans, B., Santoro, N.: Sense of direction: definitions, properties, and classes. Networks 32(3), 165–180 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  68. Flocchini, P., Mans, B., Santoro, N.: Sense of direction in distributed computing. Theor. Comput. Sci. 291, 29–53 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  69. Flocchini, P., Santoro, N.: Distributed security algorithms by mobile agents. In: Chaudhuri, S., Das, S.R., Paul, H.S., Tirthapura, S. (eds.) ICDCN 2006. LNCS, vol. 4308, pp. 1–14. Springer, Heidelberg (2006). https://doi.org/10.1007/11947950_1

    Chapter  Google Scholar 

  70. Flocchini, P., Santoro, N.: Distributed security algorithms for mobile agents. In: Sao, J., Das, S. (eds.) Mobile Agents in Networking and Distributed Computing. Wiley, Hoboken (2012)

    Google Scholar 

  71. Foukia, N., Hulaas, J.G., Harms, J.: Intrusion detection with mobile agents. In: Proceedings of 11th Annual Conference of the Internet Society (2001)

    Google Scholar 

  72. Fraigniaud, P., Gasieniec, L., Kowalski, D., Pelc, A.: Collective tree exploration. Networks 48, 166–177 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  73. Fraigniaud, P., Ilcinkas, D.: Digraphs exploration with little memory. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 246–257. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24749-4_22

    Chapter  Google Scholar 

  74. Garey, M.R., Johnson, D.S., Tarjan, R.E.: The planar hamiltonian circuit problem is NP-complete. SIAM J. Comput. 5(4), 704–714 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  75. Glaus, P.: Locating a black hole without the knowledge of incoming link. In: Dolev, S. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 128–138. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05434-1_13

    Chapter  Google Scholar 

  76. Greenberg, M.S., Byington, J.C., Harper, D.G.: Mobile agents and security. IEEE Commun. Mag. 36(7), 76–85 (1998)

    Article  Google Scholar 

  77. Hohl, F.: Time limited blackbox security: protecting mobile agents from malicious hosts. In: Vigna, G. (ed.) Mobile Agents and Security. LNCS, vol. 1419, pp. 92–113. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-68671-1_6

    Chapter  Google Scholar 

  78. Hohl, F.: A framework to protect mobile agents by using reference states. In: Proceedings of 20th International Conference on Distributed Computing Systems, pp. 410–417 (2000)

    Google Scholar 

  79. Jansen, W.: Countermeasures for mobile agent security. Comput. Commun. 23(17), 1667–1676 (2000)

    Article  Google Scholar 

  80. Kann, V.: Minimum steiner tree. http://www.nada.kth.se/~viggo/wwwcompendium/node78.html

  81. Supriya, K.M.: Mobile ad hoc netwoks security attacks and secured routing protocols: a survey. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds.) CCSIT 2012. LNICST, vol. 84, pp. 119–124. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27299-8_14

    Chapter  Google Scholar 

  82. Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Hardness and approximation results for black hole search in arbitrary graphs. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 200–215. Springer, Heidelberg (2005). https://doi.org/10.1007/11429647_17

    Chapter  MATH  Google Scholar 

  83. Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Hardness and approximation results for black hole search in arbitrary graphs. Theor. Comput. Sci. 384(2–3), 201–221 (2007)

    Article  MATH  Google Scholar 

  84. Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Approximation bounds for black hole search problems. Networks 52(4), 216–226 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  85. Kosowski, A., Navarra, A., Pinotti, C.M.: Synchronization helps robots to detect black holes in directed graphs. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 86–98. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10877-8_9

    Chapter  Google Scholar 

  86. Kosowski, A., Navarra, A., Pinotti, C.M.: Synchronous black hole search in directed graphs. Theor. Comput. Sci. 412(41), 5752–5759 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  87. Královič, R., Miklík, S.: Periodic data retrieval problem in rings containing a malicious host. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 157–167. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13284-1_13

    Chapter  Google Scholar 

  88. Lange, D., Oshima, M.: Seven good reasons for mobile agents. Commun. ACM 42(3), 88–89 (1999)

    Article  Google Scholar 

  89. Luccio, F., Pagli, L., Santoro, N.: Network decontamination with local immunization. In: Proceedings of 8th Workshop on Advances in Parallel and Distributed Computational Models (2006)

    Google Scholar 

  90. Markou, E.: Identifying hostile nodes in networks using mobile agents. Bull. Eur. Assoc. Theor. Comput. Sci. 108, 93–129 (2012)

    MATH  Google Scholar 

  91. Markou, E., Paquette, M.: Black hole search and exploration in unoriented tori with synchronous scattered finite automata. In: Baldoni, R., Flocchini, P., Binoy, R. (eds.) OPODIS 2012. LNCS, vol. 7702, pp. 239–253. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35476-2_17

    Chapter  Google Scholar 

  92. Miklík, S.: Exploration in faulty networks. Ph.D. thesis, Comenius University (2010)

    Google Scholar 

  93. Ng, S., Cheung, K.: Protecting mobile agents against malicious hosts by intention of spreading. In: Proceedings of International Conference on Parallel and Distributed Processing and Applications, pp. 725–729 (1999)

    Google Scholar 

  94. Oppliger, R.: Security issues related to mobile code and agent-based systems. Comput. Commun. 22(12), 1165–1170 (1999)

    Article  Google Scholar 

  95. Panaite, P., Pelc, A.: Exploring unknown undirected graphs. J. Algorithms 33, 281–295 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  96. Peng, M., Shi, W., Corriveau, J.-P.: Repairing faulty nodes and locating a dynamically spawned black hole search using tokens. In: IEEE Conference on Communications and Network Security, pp. 136–145. IEEE (2018)

    Google Scholar 

  97. Peng, M., Shi, W., Corriveau, J.-P., Pazzi, R., Wang, Y.: Black hole search in computer networks: state-of-the-art, challenges and future directions. J. Parallel Distrib. Comput. 88, 1–15 (2016)

    Article  Google Scholar 

  98. Prencipe, G.: Corda: distributed coordination of a set of autonomous mobile robots. In: Proceedings of 4th European Research Seminar on Advances in Distributed Systems, pp. 185–190 (2001)

    Google Scholar 

  99. Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: Proceedings of 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 770–779 (2000)

    Google Scholar 

  100. Rollik, H.: Automaten in planaren graphen. Acta Informatica 13, 287–298 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  101. Sander, T., Tschudin, C.F.: Protecting mobile agents against malicious hosts. In: Vigna, G. (ed.) Mobile Agents and Security. LNCS, vol. 1419, pp. 44–60. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-68671-1_4

    Chapter  Google Scholar 

  102. Schelderup, K., Ølnes, J.: Mobile agent security—issues and directions. In: Zuidweg, H., Campolargo, M., Delgado, J. (eds.) IS&N 1999. LNCS, vol. 1597, pp. 155–167. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48888-X_16

    Chapter  Google Scholar 

  103. Sen, J., Chandra, M.G., Harihara, S., Reddy, H., Balamuralidhar, P.: A mechanism for detection of gray hole attack in mobile ad hoc networks. In: 2007 6th International Conference on Information, Communications & Signal Processing, pp. 1–5. IEEE (2007)

    Google Scholar 

  104. Shannon, C.E.: Presentation of a maze-solving machine. In: Proceedings of 8th Conference of the Josiah Macy Jr. Foundation (Cybernetics), pp. 173–180 (1951)

    Google Scholar 

  105. Shi, W.: Black hole search with tokens in interconnected networks. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 670–682. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05118-0_46

    Chapter  Google Scholar 

  106. Shi, W., Garcia-Alfaro, J., Corriveau, J.-P.: Searching for a black hole in interconnected networks using mobile agents and tokens. J. Parallel Distrib. Comput. 74(1), 1945–1958 (2014)

    Article  Google Scholar 

  107. Shi, W., Peng, M., Corriveau, J.-P., Croft, W.L.: Faulty node repair and dynamically spawned black hole search. In: Deng, R., Weng, J., Ren, K., Yegneswaran, V. (eds.) SecureComm 2016. LNICST, vol. 198, pp. 144–162. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59608-2_8

    Chapter  Google Scholar 

  108. Spafford, E.H., Zamboni, D.: Intrusion detection using autonomous agents. Comput. Netw. 34(4), 547–570 (2000)

    Article  Google Scholar 

  109. Su, M.-Y.: Prevention of selective black hole attacks on mobile ad hoc networks through intrusion detection systems. Comput. Commun. 34(1), 107–117 (2011)

    Article  Google Scholar 

  110. Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  111. Vitek, J., Castagna, G.: Mobile computations and hostile hosts. In: Tsichritzis, D. (ed.) Mobile Objects, pp. 241–261. University of Geneva (1999)

    Google Scholar 

  112. Zarrad, A., Daadaa, Y.: A review of computation solutions by mobile agents in an unsafe environment. Int. J. Adv. Comput. Sci. Appl. 4(4), 87–92 (2013)

    Google Scholar 

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Authors and Affiliations

  1. University of Thessaly, Lamia, Greece

    Euripides Markou

  2. Carleton University, Ottawa, Canada

    Wei Shi

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  1. Euripides Markou
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  2. Wei Shi
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  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Pisa, Pisa, Italy

    Giuseppe Prencipe

  3. Carleton University, Ottawa, ON, Canada

    Nicola Santoro

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Markou, E., Shi, W. (2019). Dangerous Graphs. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_18

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