Solving a k-Node Minimum Label Spanning Arborescence Problem to Compress Fingerprint Templates

  • Andreas M. Chwatal
  • Günther R. Raidl
  • Karin Oberlechner


We present a novel approach for compressing relatively small unordered data sets by means of combinatorial optimization. The application background comes from the field of biometrics, where the embedding of fingerprint template data into images by means of watermarking techniques requires extraordinary compression techniques. The approach is based on the construction of a directed tree, covering a sufficient subset of the data points. The arcs are stored via referencing a dictionary, which contains “typical” arcs w.r.t. the particular tree solution. By solving a tree-based combinatorial optimization problem we are able to find a compact representation of the input data. As optimization method we use on the one hand an exact branch-and-cut approach, and on the other hand heuristics including a greedy randomized adaptive search procedure (GRASP) and a memetic algorithm. Experimental results show that our method is able to achieve higher compression rates for fingerprint (minutiae) data than several standard compression algorithms.


Combinatorial optimization Metaheuristics GRASP Memetic algorithm Biometric template compression Fingerprint minutiae Unordered data set compression 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Burrows, M., Wheeler, D.J.: A block-sorting lossless data compression algorithm. Technical report 124, Digital SRC Research Report (1994)Google Scholar
  3. 3.
    Chang, R.-S., Leu, S.-J.: The minimum labeling spanning trees. Inf. Process. Lett. 63(5), 277–282 (1997)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Cherkassky, B.V., Goldberg, A.V.: On implementing the push-relabel method for the maximum flow problem. Algorithmica 19(4), 390–410 (1997)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chwatal, A.M., Raidl, G.R.: Applying branch-and-cut for compressing fingerprint templates (short abstract). In: Proceedings of the European Conference on Operational Research (EURO) XXII, Prague (2007)Google Scholar
  6. 6.
    Chwatal, A.M., Raidl, G.R., Dietzel, O.: Compressing fingerprint templates by solving an extended minimum label spanning tree problem. In: Proceedings of the Seventh Metaheuristics International Conference (MIC), Montreal (2007)Google Scholar
  7. 7.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT, Cambridge (2001)MATHGoogle Scholar
  8. 8.
    Dietzel, O.: Combinatorial optimization for the compression of biometric templates. Master’s thesis, Vienna University of Technology, Institute of Computer Graphics and Algorithms (2008)Google Scholar
  9. 9.
    Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Garris, M.D., McCabe, R.M.: NIST special database 27: fingerprint minutiae from latent and matching tenprint images. Technical report, National Institute of Standards and Technology (2000)Google Scholar
  11. 11.
    Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and vlsi. J. ACM 32(1), 130–136 (1985)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    ILOG Concert Technology, CPLEX: ILOG. Version 11.0 (2009)
  13. 13.
    Jain, A., Uludag, U.: Hiding fingerprint minutiae in images. In: Proceedings of Third Workshop on Automatic Identification Advanced Technologies, pp. 97–102 (2002)Google Scholar
  14. 14.
    Krumke, S.O., Wirth, H.-C.: On the minimum label spanning tree problem. Inf. Process. Lett. 66(2), 81–85 (1998)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Library for Efficient Datastructures and Algorithms (LEDA): Algorithmics Solutions Software GmbH. Version 5.1 (2009)
  16. 16.
    Magnanti, T., Wolsey, L.: Optimal trees. In: Network Models. Handbook in Operations Research and Management Science, pp. 503–615. North Holland, Amsterdam (1995)Google Scholar
  17. 17.
    Maltoni, D., Maio, D., Jain, A.K., Prabhakar, S.: Handbook of Fingerprint Recognition. Springer, New York (2003)MATHGoogle Scholar
  18. 18.
    Moffat, A., Neal, R.M., Witten, I.H.: Arithmetic coding revisited. ACM Trans. Inf. Sys. 16(3), 256–294 (1998)CrossRefGoogle Scholar
  19. 19.
    Nummela, J., Julstrom, B.A.: An effective genetic algorithm for the minimum-label spanning tree problem. In: GECCO ’06: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 553–558. ACM, New York (2006)CrossRefGoogle Scholar
  20. 20.
    Raidl, G.R., Chwatal, A.: Fingerprint template compression by solving a minimum label k-node subtree problem. In: Simos, E. (ed.) Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, vol. 936, pp. 444–447. American Institute of Physics, New York (2007)Google Scholar
  21. 21.
    Saleh, A., Adhami, R.: Curvature-based matching approach for automatic fingerprint identification. In: Proceedings of the Southeastern Symposium on System Theory, pp. 171–175 (2001)Google Scholar
  22. 22.
    Sayood, K.: Introduction to Data Compression, 3rd edn. Morgan Kaufmann, San Mateo (2006)Google Scholar
  23. 23.
    Varshney, L.R., Goyal, V.K.: Benefiting from disorder: source coding for unordered data. arXiv, abs/0708.2310 (2007)Google Scholar
  24. 24.
    Vitter, J.S.: Design and analysis of dynamic huffman codes. J. ACM 34(4), 825–845 (1987)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Wolsey, L.A., Nemhauser, G.L.: Integer and Combinatorial Optimization. Wiley-Interscience, New York (1999)MATHGoogle Scholar
  26. 26.
    Xiong, Y., Golden, B., Wasil, E.: A one-parameter genetic algorithm for the minimum labeling spanning tree problem. IEEE Trans. Evol. Comput. 9(1), 55–60, 2 (2005)CrossRefGoogle Scholar
  27. 27.
    Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3), 337–343 (1977)MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Ziv, J., Lempel, A.: Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5), 530–536 (1978)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Andreas M. Chwatal
    • 1
  • Günther R. Raidl
    • 1
  • Karin Oberlechner
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

Personalised recommendations