On Asymptotically Optimal Approach for Finding of the Minimum Total Weight of Edge-Disjoint Spanning Trees with a Given Diameter

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Acesso é pago ou somente para assinantes

Resumo

We consider the intractable problem of finding several edge-disjoint spanning trees of the minimum total weight with a given diameter in complete undirected graph in current paper. The weights of edges of a graph are random variables from several continuous distributions: uniform, biased truncated exponential, biased truncated normal. The approximation algorithm with time complexity O(n2), where n is number of vertices in graph, is proposed for solving this problem. The asymptotic optimality conditions for constructed algorithm is presented for each considered probabilistic distribution.

Sobre autores

E. Gimadi

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Email: gimadi@math.nsc.ru
Novosibirsk, Russia

A. Shtepa

Novosibirsk State University

Autor responsável pela correspondência
Email: shoomath@gmail.com
Novosibirsk, Russia

Bibliografia

  1. Frieze A. On the Value of a Random MST Problem // Discrete Applied Mathematics. 1985. V. 10. P. 47-56. https://doi.org/10.1016/0166-218X(85)90058-7
  2. Angel O., Flaxman A.D., Wilson D.B. A Sharp Threshold for Minimum Bounded-Depth and Bounded-Diameter Spanning Trees and Steiner Trees in Random Networks // Combinatorica. 2012. V. 32. P. 1-33. https://doi.org/10.1007/s00493-012-2552-z
  3. Cooper C., Frieze A., Ince N., Janson S., Spencer J. On the Length of a Random Minimum Spanning Tree // Combinatorics, Probability and Computing. 2016. V. 25. No. 1. P. 89-107. https://doi.org/10.1017/S0963548315000024
  4. Garey M.R., Johnson D.S. Computers and Intractability. 1979. Freeman, San Francisco. 340 p.
  5. Clementi A.E.F., Ianni M.D., Monti A., Rossi, G., Silvestri R. Experimental Analysis of Practically E cient Algorithms for Bounded-Hop Accumulation in Ad-Hoc Wireless Networks // Proc. 19th IEEE Int. Parallel Distributed Processing Symposium (IPDPS'05). 2005. P. 8-16. https://doi.org/10.1109/IPDPS.2005.210
  6. Bala K., Petropoulos K., Stern T.E. Multicasting in a Linear Lightwave Network // Proc. of IEEE INFOCOM'93. 1993. P. 1350-1358. https://doi.org/10.1109/INFCOM.1993.253399
  7. Bookstein A., Klein S.T. Compression of Correlated Bit-Vectors // Inform. Syst. 1996. V. 16. No. 4. P. 110-118.
  8. Raymond K. A Tree-Based Algorithm for Distributed Mutual Exclusion // ACM Trans. on Comput. Syst. 1989. V. 7. No. 1. P. 61-77. https://doi.org/10.1145/58564.59295
  9. Gruber M. Exact and Heuristic Approaches for Solving the Bounded Diameter Minimum Spanning Tree Problem. Vienna University of Technology. PhD Thesis. 2009.
  10. Gimadi E.Kh., Serdyukov A.I. A Probabilistic Analysis of Approximation Algorithm for the Minimum Weight Spanning Tree Problem with a Bounded Below Diameter / Oper. Res. Proceed. V. 99. In: K. Inderfurth et. al. (eds.). Springer, Berlin. 2000. P. 63-68. https://doi.org/10.1007/978-3-642-58300-1_12
  11. Gimadi E.Kh., Istomin A.M., Shin E.Yu. On Algorithm for the Minimum Spanning Tree Problem Bounded Below // Proc. conference DOOR 2016. Vladivostok. Russia. CEUR-WS. V. 1623. 2016. P. 11-17.
  12. Gimadi E.Kh., Shin E.Yu. On Given Diameter MST Problem on Random Input Data / In: I. Bykadorov, V. Strusevich, T. Tchemisova (eds.). MOTOR 2019. Communications in Computer and Information Science. V. 1090. Springer, Cham. 2019. P. 30-38. https://doi.org/10.1007/978-3-030-33394-2_3
  13. Gimadi E.Kh., Shevyakov A.S., Shtepa A.A. A Given Diameter MST on a Random Graph / In: N. Olenev, Y. Evtushenko, M. Khachay, V. Malkova (eds.). Optimization and Applications - 11th International Conference OPTIMA. 2020. LNCS. V. 12422. P. 110-121. https://doi.org/10.1007/978-3-030-62867-3_9
  14. Гимади Э.Х., Глебов Н.И., Перепелица В.А. Алгоритмы с оценками для задач дискретной оптимизации // Проблемы кибернетики. 1975. Вып. 31. С. 35-42.
  15. Petrov V.V. Limit Theorems of Probability Theory. Sequences of Independent Random Variables. 1995. Clarendon Press. Oxford. 304 p.
  16. Гимади Э.Х., Глазков Ю.В. Об асимптотически точном алгоритме решения одной модификации трехиндексной планарной задачи о назначениях // Дискретный анализ и исследование операций. 2006. Сер. 2. Т. 13. № 1. С. 10-26.
  17. Гимади Э.Х., Хачай М.Ю. Экстремальные задачи на множествах перестановок. Екатеринбург: Изд-во УМЦ УПИ, 2016. 219 c.
  18. Гимади Э.Х., Шин Е.Ю. Вероятностный анализ алгоритма нахождения в графе минимального остовного дерева с ограниченным снизу диаметром // Дискретный анализ и исследование операций. 2015. Т. 22. № 4. С. 5-20. https://doi.org/10.17377/daio.2015.22.474

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar

Declaração de direitos autorais © The Russian Academy of Sciences, 2023