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The Complexity of Finding a Broadcast Center

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Algorithmic Aspects in Information and Management (AAIM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13153))

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Abstract

Broadcasting in networks is one of the most important information dissemination processes. It is known that finding the optimal (minimum) broadcast time is NP-hard. Some of the follow-up researches focus on approximations/heuristics to find the broadcast center, a set of nodes from which the broadcast time in the network is minimum, in a given network by assuming the problem is hard without an actual proof. In this paper, we show that answering the questions “is a set of vertices a broadcast center to the given graph”, and “does the given graph has a broadcast center of size smaller than k” are both NP-hard under Turing reductions.

Granted by the Guangdong Provincial Innovation and Enhancement Project of China under Grant No. R5201918.

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References

  1. Averbuch, A., Shabtai, R.H., Roditty, Y.: Efficient construction of broadcast graphs. Discret. Appl. Math. 171, 9–14 (2014)

    Article  MathSciNet  Google Scholar 

  2. Bar-Noy, A., Guha, S., Naor, J.S., Schieber, B.: Multicasting in heterogeneous networks. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, (STOC), pp. 448–453. ACM (1998)

    Google Scholar 

  3. Beier, R., Sibeyn, J.F.: A powerful heuristic for telephone gossiping. In: Proceedings of the 7th Colloquium on Structural Information and Communication Complexity (SIROCCO), pp. 17–35. Carleton Scientific (2000)

    Google Scholar 

  4. Bermond, J.-C., Fraigniaud, P., Peters, J.G.: Antepenultimate broadcasting. Networks 26(3), 125–137 (1995)

    Article  MathSciNet  Google Scholar 

  5. Bermond, J.-C., Hell, P., Liestman, A.L., Peters, J.G.: Sparse broadcast graphs. Discret. Appl. Math. 36(2), 97–130 (1992)

    Article  MathSciNet  Google Scholar 

  6. Dinneen, M.J., Ventura, J.A., Wilson, M.C., Zakeri, G.: Compound constructions of broadcast networks. Discret. Appl. Math. 93(2), 205–232 (1999)

    Article  MathSciNet  Google Scholar 

  7. Elkin, M., Kortsarz, G.: Sublogarithmic approximation for telephone multicast: path out of jungle (extended abstract). In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 76–85. Society for Industrial and Applied Mathematics (2003)

    Google Scholar 

  8. Elkin, M., Kortsarz, G.: A combinatorial logarithmic approximation algorithm for the directed telephone broadcast problem. SIAM J. Comput. 35(3), 672–689 (2005)

    Article  MathSciNet  Google Scholar 

  9. Farley, A.M.: Minimal broadcast networks. Networks 9(4), 313–332 (1979)

    Article  MathSciNet  Google Scholar 

  10. Farley, A.M., Hedetniemi, S., Mitchell, S., Proskurowski, A.: Minimum broadcast graphs. Discret. Math. 25(2), 189–193 (1979)

    Article  MathSciNet  Google Scholar 

  11. Fraigniaud, P., Lazard, E.: Methods and problems of communication in usual networks. Discret. Appl. Math. 53(1–3), 79–133 (1994)

    Article  MathSciNet  Google Scholar 

  12. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)

    MATH  Google Scholar 

  13. Gargano, L., Vaccaro, U.: On the construction of minimal broadcast networks. Networks 19(6), 673–689 (1989)

    Article  MathSciNet  Google Scholar 

  14. Grigni, M., Peleg, D.: Tight bounds on mimimum broadcast networks. SIAM J. Discret. Math. 4(2), 207–222 (1991)

    Article  Google Scholar 

  15. Grigoryan, H., Harutyunyan, H.A.: New lower bounds on broadcast function. In: Gu, Q., Hell, P., Yang, B. (eds.) AAIM 2014. LNCS, vol. 8546, pp. 174–184. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07956-1_16

    Chapter  Google Scholar 

  16. Harutyunyan, H.A.: Broadcast networks with near optimal cost. In: Gu, Q., Hell, P., Yang, B. (eds.) AAIM 2014. LNCS, vol. 8546, pp. 312–322. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07956-1_28

    Chapter  Google Scholar 

  17. Harutyunyan, H.A., Li, Z.: A simple construction of broadcast graphs. In: Du, D.-Z., Duan, Z., Tian, C. (eds.) COCOON 2019. LNCS, vol. 11653, pp. 240–253. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26176-4_20

    Chapter  Google Scholar 

  18. Harutyunyan, H.A., Li, Z.: A new construction of broadcast graphs. Discret. Appl. Math. 280, 144–155 (2020)

    Article  MathSciNet  Google Scholar 

  19. Harutyunyan, H.A., Liestman, A.L.: More broadcast graphs. Discret. Appl. Math. 98(1), 81–102 (1999)

    Article  MathSciNet  Google Scholar 

  20. Harutyunyan, H.A., Liestman, A.L.: Upper bounds on the broadcast function using minimum dominating sets. Discret. Math. 312(20), 2992–2996 (2012)

    Article  MathSciNet  Google Scholar 

  21. Harutyunyan, H.A., Liestman, A.L., Peters, J.G., Richards, D.: Broadcasting and gossiping. In: Handbook of Graph Theory, pp. 1477–1494. Chapman and Hall (2013)

    Google Scholar 

  22. Harutyunyan, H.A., Liestman, A.L., Shao, B.: A linear algorithm for finding the k-broadcast center of a tree. Networks 53(3), 287–292 (2009)

    Article  MathSciNet  Google Scholar 

  23. Harutyunyan, H., Maraachlian, E.: Linear algorithm for broadcasting in unicyclic graphs. In: Lin, G. (ed.) COCOON 2007. LNCS, vol. 4598, pp. 372–382. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73545-8_37

    Chapter  Google Scholar 

  24. Harutyunyan, H.A., Maraachlian, E.: On broadcasting in unicyclic graphs. J. Comb. Optim. 16(3), 307–322 (2008)

    Article  MathSciNet  Google Scholar 

  25. Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18(4), 319–349 (1988)

    Article  MathSciNet  Google Scholar 

  26. Hromkovič, J., Klasing, R., Monien, B., Peine, R.: Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping). In: Du, D.Z., Hsu, D.F. (eds.) Combinatorial Network Theory. Applied Optimization, vol. 1, pp. 125–212. Springer, Boston (1996). https://doi.org/10.1007/978-1-4757-2491-2_5

    Chapter  Google Scholar 

  27. Čevnik, M., Žerovnik, J.: Broadcasting on cactus graphs. J. Comb. Optim. 33(1), 292–316 (2015). https://doi.org/10.1007/s10878-015-9957-8

    Article  MathSciNet  MATH  Google Scholar 

  28. Maheo, M., Saclé, J.-F.: Some minimum broadcast graphs. Discret. Appl. Math. 53(1–3), 275–285 (1994)

    Article  MathSciNet  Google Scholar 

  29. Slater, P.J., Cockayne, E.J., Hedetniemi, S.T.: Information dissemination in trees. SIAM J. Comput. 10(4), 692–701 (1981)

    Article  MathSciNet  Google Scholar 

  30. Su, Y.-H., Lin, C.-C., Lee, D.T.: Broadcasting in heterogeneous tree networks. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 368–377. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14031-0_40

    Chapter  Google Scholar 

  31. Zhou, J., Zhang, K.: A minimum broadcast graph on 26 vertices. Appl. Math. Lett. 14(8), 1023–1026 (2001)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Concordia University, Montreal, QC, H3G 1M8, Canada

    Hovhannes A. Harutyunyan

  2. Computer Science and Technology, United International College, Zhuhai, 0086-519000, China

    Zhiyuan Li

Authors
  1. Hovhannes A. Harutyunyan
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  2. Zhiyuan Li
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Correspondence to Zhiyuan Li .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

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Harutyunyan, H.A., Li, Z. (2021). The Complexity of Finding a Broadcast Center. In: Wu, W., Du, H. (eds) Algorithmic Aspects in Information and Management. AAIM 2021. Lecture Notes in Computer Science(), vol 13153. Springer, Cham. https://doi.org/10.1007/978-3-030-93176-6_6

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  • DOI: https://doi.org/10.1007/978-3-030-93176-6_6

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  • Online ISBN: 978-3-030-93176-6

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