Matrix rounding under the Lp-discrepancy measure and its application to digital halftoning

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 06-08-January-2002, Issue , 2002, Pages 896-904

  Asano, Tetsuo ^a   Katoh, Naoki ^b   Obokata, Koji ^a   Tokuyama, Takeshi ^c  

^a JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

^c TOHOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

INTEGER PROGRAMMING; MATRIX ALGEBRA; PIECEWISE LINEAR TECHNIQUES; POLYNOMIAL APPROXIMATION;

DIGITAL HALFTONING; DISCREPANCY MEASURES; INTEGER PROGRAMMING PROBLEMS; INTEGER-VALUED MATRICES; ITS APPLICATIONS; LAMINAR FAMILIES; PIECEWISE LINEAR; ROUNDING PROBLEM;

PROBLEM SOLVING;

EID: 84902475989     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. R. Ahuja, T. Magnanti, and J. Orlin: Network Flows, Theory Algorithms and Applications, Princeton Hall, 1993.
2. T. Asano, T. Matsui, and T. Tokuyama: "Optimal Roundings of Sequences and Matrices, " Nordic Journal of Computing, Vol. 7, No. 3, pp.241-256, Fall 2000.
3. T. Asano and T. Tokuyama: "How to Color a Checkerboard with a Given Distribution -Matrix Rounding Achieving Low 2x2-Discrepancy, " to appear in Proc. ISAAC01 (2001).
4. B. E. Bayer: "An optimum method for two-level rendition of continuous-tone pictures, " Conference Record, IEEE International Conf. on Communications, 1 (1973), pp.(26-ll)-(26-15).
5. Z. Baranyai: "On the factorization of the complete uniform hypergraphs", in Infinite and Finite Sets, eds. A. Hanaj, R. Rado and V. T. Sos, Colloq. Math. Soc. J'anos Bolyai 10, pp.91-108.
6. J. Beck and V. T. Sos: Discrepancy Theory, in Handbook of Combinatorics Volume II, (ed. R.Graham, M. Grotschel, and L Lovasz) 1995, Elsevier.
7. B. Doerr: "Lattice Approximation and Linear Discrepancy of Totally Unimodular Matrices-Extended Abstract-, " SIAM-ACM Symposium on Discrete Algorithms, pp.119-125, 2001.
8. J. Edmonds and R.M. Karp: "Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems, " Journal of ACM, 19, 248-264, 1972.
9. R. W. Floyd and L. Steinberg: "An adaptive algorithm for spatial gray scale, " SID 75 Digest, Society for Information Display, (1975) pp.36-37.
10. A. Ghoulia-Houri, "Characterisation des matrices totalement unimodulaires, " C.R. Acad/Sci. Paris, 254, (1962) 1192-1194.
11. D.S. Hochbaum and J.G. Shanthikumar: "Nonlinear separable optimization is not much harder than linear optimization, " Journal of ACM, Vol. 37, No. 4 (1990) 843-862.
12. A.V. Karzanov and S.T. McCormick: "Polynomial methods for separable convex optimization in totally unimodular linear spaces with applications, " SIAM J. on Computing, Vol. 26, No. 4 (1997) 1245-1275.
13. D.E. Knuth: "Digital halftones by dot diffusion, " ACM Trans. Graphics, 6-4 (1987), pp.245-273. The LEDA homepage: http://www.algorithmic-solutions.com/asJitml/products/products.html.
14. J. O. Limb: "Design of dither waveforms for quantized visual signals, " Bell Syst. Tech. J., 48-7 (1969), pp. 2555-2582.
15. B. Lippel and M. Kurland: "The effect of dither on luminance quantization of pictures, " IEEE Trans. Commun. Tech., COM-19 (1971), pp.879-888.
16. M. Minoux: "Solving Integer Minimum Cost Flows with Separable Cost Objective Polynomially, " Mathematical Programming Study 26 (1986) pp.237-239
17. K. Sadakane, N. Takki-Chebihi, and T. Tokuyama: "Combinatorics and Algorithms on Low-Discrepancy Roundings of a Real Sequence", Proc. 28th ICALP, Springer LNCS2076, (2001) pp. 166-177.
18. A. Schrijver: "Theory of Linear and Integer Programming, " Wiley-Interscience Series in Discrete Mathematics , John Wily and Sons (1986).