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The Minimum Routing Cost Tree Problem

State of the art and a core-node based heuristic algorithm

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Abstract

The minimum routing cost tree problem arises when we need to find the tree minimizing the minimum travel/communication cost, i.e., the tree which presents the minimal difference with the same cost computed on the whole network. This paper provides the state of the art of the problem and proposes a new heuristic based on the identification of a core of the network around which the solution can be built. The algorithm has been tested on literature instances of up to one thousand nodes. The results, compared with those of other heuristic algorithms, prove the competitiveness of the proposed one both in terms of the quality of the solution and computation time.

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References

  • Beasley JE (1990) OR-library: distributing test problems by electronic mail. J Oper Res Soc 41:1069–1072

    Article  Google Scholar 

  • Campos R, Ricardo M (2008) A fast algorithm for computing minimum routing cost spanning trees. Comput Netw 52:3229–3247

    Article  MATH  Google Scholar 

  • Chen Y H, Liao G L, Tang C Y (2007) Approximation algorithms for 2-source minimum routing cost k-tree problems. In: Computational science and its applications, ICCSA 2007. Springer, Berlin, pp 520–533

  • Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1:269–271

    Article  MathSciNet  MATH  Google Scholar 

  • Fernndez E, Luna-Mota C, Hildenbrandt A, Reinelt G, Wiesberg S (2013) A flow formulation for the optimum communication spanning tree. Electron Notes Discrete Math 41:85–92

    Article  Google Scholar 

  • Fischetti M, Lancia G, Serafini P (2002) Exact algorithms for minimum routing cost trees, networks. Wiley, London, pp 161–173

    MATH  Google Scholar 

  • Hieu NM, Quoc PT, Nghia ND (2011) An approach of ant algorithm for solving minimum routing cost spanning tree problem. In: Proceedings of the second symposium on information and communication technology, SoICT11. ACM, New York, pp 5–10

  • Hu TC (1974) Optimum communication spanning trees. J Comput SIAM 3:188–195

    Article  MathSciNet  MATH  Google Scholar 

  • Johnson DS, Lenstra JK, Rinnooy Kan AHG (1978) The complexity of the network design problem. Networks 8:279–285

    Article  MathSciNet  MATH  Google Scholar 

  • Julstrom BA (2001) The blob code: a better string coding of spanning trees for evolutionary search. In: Wu AS (ed) 2001 Genetic and evolutionary computation conference workshop program, San Francisco, CA, pp 256–261

  • Julstrom BA (2005) The Blob code is competitive with edgesets in genetic algorithms for the minimum routing cost spanning tree problem. In: Beyer H-G et al (eds) Proceedings of the genetic and evolutionary computation conference 2005, vol 1. ACM Press, New York, pp 585–590

    Google Scholar 

  • Kim T, Seob SC, Kim D (2015) Distributed formation of degree constrained minimum routing cost tree in wireless ad-hoc networks. J Parallel Distrib Comput 83:143–158

    Article  Google Scholar 

  • Lin CW, Wu BY (2017) On the minimum routing cost clustered tree problem. J Comb Optim 33(6):1106–1121

    Article  MathSciNet  MATH  Google Scholar 

  • Merz P, Wolf S (2006) Evolutionary local search for designing peer-to-peer overlay topologies based on minimum routing cost spanning trees, parallel problem solving from nature-PPSN IX. Springer, Berlin, pp 272–281

    Google Scholar 

  • Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36:1389–1401

    Article  Google Scholar 

  • Raidl GR, Julstrom BA (2003) Edge sets: an effective evolutionary coding of spanning trees. IEEE Trans Evol Comput 7:225–239

    Article  Google Scholar 

  • Sattari S, Didehvar F (2015) A metaheuristic algorithm for the minimum routing cost spanning tree problem. Iran J Oper Res 6(1):65–78

    Google Scholar 

  • Sattari S, Didehvar F (2013) Variable neighborhood search approach for the minimum routing cost spanning tree problem. Int J Oper Res 10(4):153–160

    MathSciNet  Google Scholar 

  • Singh A (2008) A new heuristic for the minimum routing cost spanning tree problem. In: Proceedings of 11th international conference on information technology. IEEE Computer Society, pp. 9–13

  • Singh A, Sundar S (2011) An artificial bee colony algorithm for the minimum routing cost spanning tree problem. Soft Comput Fus Found Methodol Appl 15(12):2489–2499

    Google Scholar 

  • Tan QP (2012a) A Heuristic approach for solving the minimum routing cost spanning tree problem. Int J Mach Learn Comput, IACSIT 2:406–409

    Article  Google Scholar 

  • Tan QP (2012b) A genetic approach for solving minimum routing cost spanning tree problem. Int J Mach Learn Comput 2(4):410–414

    Article  Google Scholar 

  • Tan QP, Due NN (2013) An experimental study of minimum routing cost spanning tree algorithms. In: International conference of soft computing and pattern recognition (SoCPaR). IEEE Computer Society, pp 158–165

  • Wolf S, Merz P (2010) Efficient cycle search for the minimum routing cost spanning tree problem. Lect Notes Comput Sci 6022:276–287

    Article  MathSciNet  Google Scholar 

  • Wong R (1980) Worst-case analysis of network design problem heuristics, SIAM. J Algebr Discr Methods 1:51–63

    Article  MATH  Google Scholar 

  • Wu BY, Lancia G, Bafna V, Chao KM, Ravi R, Tang CY (1999) A polynomial-time approximation scheme for minimum routing cost spanning trees. SIAM J Comp 29:761–778

    Article  MathSciNet  MATH  Google Scholar 

  • Wu BY, Chao KM, Tang CY (2000) Approximation algorithms for some optimum communication spanning tree problems. Discrete Appl Math 102(3):245–266

    Article  MathSciNet  MATH  Google Scholar 

  • Wu BY (2002) A polynomial time approximation scheme for the two-source minimum routing cost spanning trees. J Algorithms 44(2):359–378

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Correspondence to Adriano Masone.

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Conflict of interest

Adriano Masone declares that he has no conflict of interest. Antonio Sforza declares that he has no conflict of interest. Maria Elena Nenni declares that she has no conflict of interest.

Funding

The research activity of the authors was partially funded by the Department of Electrical Engineering and Information Technology and by the University Federico II of Naples, within the OPT_APP for EPG project (Optimization Approaches for designing and protecting Electric Power Grid) and MOSTOLOG project (A multi-objective approach for Sustainable Logistic System, DIETI-ALTRI_DR408_2017_Ricerca di Ateneo).

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This article does not contain any studies with human or animals performed by any of the authors.

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Communicated by P. Beraldi, M. Boccia, C. Sterle.

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Masone, A., Nenni, M.E., Sforza, A. et al. The Minimum Routing Cost Tree Problem. Soft Comput 23, 2947–2957 (2019). https://doi.org/10.1007/s00500-018-3557-3

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