Constraint-Based Local Search for Golomb Rulers

  • M. M. Alam PolashEmail author
  • M. A. Hakim Newton
  • Abdul Sattar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9075)


This paper presents a constraint-based local search algorithm to find an optimal Golomb ruler of a specified order. While the state-of-the-art search algorithms for Golomb rulers hybridise a range of sophisticated techniques, our algorithm relies on simple tabu meta-heuristics and constraint-driven variable selection heuristics. Given a reasonable time limit, our algorithm effectively finds 16-mark optimal rulers with success rate 60 % and 17-mark rulers with 6 % near-optimality.


Golomb ruler Constraints Local search Tabu meta-heuristics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ayari, N., Jemai, A.: Parallel hybrid evolutionary search for Golomb ruler problem. In: International Conference on Metaheuristics and Nature Inspired Computing (META) (2010)Google Scholar
  2. 2.
    Ayari, N., Luong, T., Jemai, A.: A hybrid genetic algorithm for golomb ruler problem. In: IEEE/ACS International Conference on Computer Systems and Applications (AICCSA), pp. 1–4 (2010)Google Scholar
  3. 3.
    Babcock, W.: Intermodulation interface in radio systems. Bell Systems Technical Journal, 63–73 (1953)Google Scholar
  4. 4.
    Bloom, G., Golomb, S.: Application of numbered undirected graphs. In: Proceedings of the IEEE, vol. 65(4), pp. 562–570 (1977)Google Scholar
  5. 5.
    Blum, E., Biraud, F., Ribes, J.: On optimal synthetic linear arrays with applications to radioastronomy. IEEE Transactions on Anntenas and Propagation (1974)Google Scholar
  6. 6.
    Cai, S., Su, K., Sattar, A.: Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artificial Intelligence 175(9–10), 1672–1696 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Cotta, C., Dotu, I., Fernandez, A.J., Hentenryck, P.V.: Local search based hybrid algorithm for finding Golomb rulers. Contraints, 263–291 (2007)Google Scholar
  8. 8.
    Dollas, A., Rankin, W., McCracken, D.: A new algorithm for Golomb ruler derivation and proof of the 19-mark ruler. IEEE Transactions on Information Theory, 379–386 (1998)Google Scholar
  9. 9.
    Dotu, I., Hentenryck, P.V.: A simple hybrid evolutionary algorithm for finding Golomb rulers. IEEE Congress on Evolutionary Computation (2005)Google Scholar
  10. 10.
    Drakakis, K.: A review of the available construction methods for Golomb rulers. Advances in Mathematics of Communications 3(3), 235–250 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Feeny, B.: Determining optimum and near-optimum Golomb rulers using genetic algorithms. Master’s thesis, Computer Science, University College Cork, October 2003Google Scholar
  12. 12.
    Galinier, P., Jaumard, B., Morales, R., Pesant, G.: A constraint-based approach to the golomb ruler problem. In: 3rd International Workshop on CPAIOR (2001)Google Scholar
  13. 13.
    Klove, T.: Bounds and construction for difference triangle sets. IEEE Transactions on Information Theory, 879–886 (1989)Google Scholar
  14. 14.
    Newton, M.A.H., Pham, D.N., Sattar, A., Maher, M.: Kangaroo: an efficient constraint-based local search system using lazy propagation. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 645–659. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  15. 15.
    Prestwich, S.: Trading completeness for scalability: hybrid search for cliques and rulers. In: 3rd International workshop on CPAIOR, pp. 159–174 (2001)Google Scholar
  16. 16.
    Rankin, W.: Optimal Golomb rulers: An exhaustive parallel search implementation. Master’s thesis, Duke University Electrical Engineering Dept., Durham, NC, December 1993Google Scholar
  17. 17.
    Robbins, J., Gagliardi, R., Taylor, H.: Acquisition sequences in PPM communications. IEEE Transactions on Information Theory, 738–744 (1987)Google Scholar
  18. 18.
    Robinson, J., Bernstein, A.: A class of binary recurrent codes with limited error propagation. IEEE Transactions on Information Theory, 106–113 (1967)Google Scholar
  19. 19.
    Shearer, J.: Some new optimum Golomb rulers. IEEE Transactions on Information Theory, 183–184 (1990)Google Scholar
  20. 20.
    Smith, B., Walsh, T.: Modelling the golomb ruler problem. In: Workshop on Non-Binary Constraints (IJCAI), Stockholm (1999)Google Scholar
  21. 21.
    Soliday, S., Homaifar, A., Lebby, G.: Genetic algorithm approach to the search for golomb rulers. In: Eshelman, L.J. (ed.) 6th International Conference on Genetic Algorithm (ICGA 1995), pp. 528–535. Morgan Kaufmann, Pittsburg (1995)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • M. M. Alam Polash
    • 1
    Email author
  • M. A. Hakim Newton
    • 1
  • Abdul Sattar
    • 1
    • 2
  1. 1.Institute for Integrated and Intelligent SystemsGriffith UniversityNathanAustralia
  2. 2.Queensland Research Lab, National ICT AustraliaSydneyAustralia

Personalised recommendations