Abstract
We study the problem of black hole search by a set of mobile agents, where the underlying graph is a dynamic cactus. A black hole is a dangerous vertex in the graph that eliminates any visiting agent without leaving any trace behind. Key parameters that dictate the complexity of finding the black hole include: the number of agents required (termed as size), the number of moves performed by the agents in order to determine the black hole location (termed as move) and the time (or round) taken to terminate. This problem has already been studied where the underlying graph is a dynamic ring [6]. In this paper, we extend the same problem to a dynamic cactus. We introduce two categories of dynamicity, but still, the underlying graph needs to be connected: first, we examine the scenario where, at most, one dynamic edge can disappear or reappear at any round. Secondly, we consider the problem for at most k dynamic edges. In both scenarios, we establish lower and upper bounds for the necessary number of agents, moves and rounds.
A. Bhattacharya—Supported by CSIR, Govt. of India, Grant Number: 09/731(0178)/ 2020-EMR-I
P. S. Mandal—This work was done while Partha Sarathi Mandal was in the position of Visiting Professor at Luiss University, Rome, Italy.
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Bhattacharya, A., Italiano, G.F., Mandal, P.S.: Black hole search in dynamic cactus graph (2023). https://doi.org/10.48550/arXiv.2311.10984
Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Complexity of searching for a black hole. Fund. Inform. 71(2–3), 229–242 (2006)
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)
Di Luna, G., Dobrev, S., Flocchini, P., Santoro, N.: Distributed exploration of dynamic rings. Distrib. Comput. 33, 41–67 (2020)
Di Luna, G.A., Flocchini, P., Pagli, L., Prencipe, G., Santoro, N., Viglietta, G.: Gathering in dynamic rings. Theor. Comput. Sci. 811, 79–98 (2020)
Di Luna, G.A., Flocchini, P., Prencipe, G., Santoro, N.: Black hole search in dynamic rings. In: 2021 IEEE 41st International Conference on Distributed Computing Systems (ICDCS), pp. 987–997. IEEE (2021)
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks: optimal mobile agents protocols. Distrib. Comput. 19 (2006)
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(06), 1355–1372 (2008)
Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Searching for black holes in subways. Theory Comput. Syst. 50, 158–184 (2012)
Fraigniaud, P., Ilcinkas, D., Peer, G., Pelc, A., Peleg, D.: Graph exploration by a finite automaton. Theor. Comput. Sci. 345(2–3), 331–344 (2005)
Gotoh, T., Flocchini, P., Masuzawa, T., Santoro, N.: Exploration of dynamic networks: tight bounds on the number of agents. J. Comput. Syst. Sci. 122, 1–18 (2021)
Gotoh, T., Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T.: Exploration of dynamic tori by multiple agents. Theor. Comput. Sci. 850, 202–220 (2021)
Gotoh, T., Sudo, Y., Ooshita, F., Masuzawa, T.: Dynamic ring exploration with (h, s) view. Algorithms 13(6), 141 (2020)
Ilcinkas, D., Wade, A.M.: Exploration of dynamic cactuses with sub-logarithmic overhead. Theory Comput. Syst. 65, 257–273 (2021)
Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: Proceedings of the Forty-Second ACM Symposium on Theory of Computing, pp. 513–522 (2010)
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.) Principles of Distributed Systems. OPODIS 2012. LNCS, vol. 7702, pp. 239–253. Springer, Berlin, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35476-2_17
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Bhattacharya, A., Italiano, G.F., Mandal, P.S. (2024). Black Hole Search in Dynamic Cactus Graph. In: Uehara, R., Yamanaka, K., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2024. Lecture Notes in Computer Science, vol 14549. Springer, Singapore. https://doi.org/10.1007/978-981-97-0566-5_21
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