Publikationen

Books

  • Discrete structures in biomathematics - An introduction for application. Shaker Verlag, Aachen, 2006 (182 + x Seiten)
  • Shortest Connectivity - An Introduction with Application in Phylogeny. Springer Science & Media, Inc., 2005 (268 + xi pages)
  • The Steiner Ratio. Kluwer Acadamic Publishers, Dordrecht, Boston, London, 2001 (244 + xii pages)
  • Steiner Minimal Trees. Kluwer Acadamic Publishers, Dordrecht, Boston, London, 1998 (319 + xi pages)

Articles

  • The Steiner ratio of high-dimensional Banach-Minkowski spaces. Discrete Applied Mathematics, 138 (2004), 29-34
  • The Steiner ratio for manifolds (Russian, together with A. O. Ivanov and A. A. Tuzhilin), Mat. Zametki, 74 (2003), 387-395
  • Connectivity Calculus. (together with A. Dress, K. Huber and V. Moulton), Applied Mathematics Letters, 16 (2003), 395-399
  • The Steiner Ratio of several Discrete Metric Spaces. Discrete Mathematics, 260 (2003), 189-196
  • Embedding Complexity and Discrete Optimization II: A Dynamical Programming Approach to the Steiner Tree Problem. (zusammen mit A. Dress, K. Huber und V. Moulton) Annals of Combinatorics, 6(2002), 275-283
  • Embedding Complexity and Discrete Optimization I: A A New Divide&Conquer Approach to Discrete Optimization. (zusammen mit A. Dress, K. Huber und V. Moulton) Annals of Combinatorics, 6(2002), 257-273
  • Melzak's algorithm for phylogenetic spaces. (Russian) (zusammen mit A. O. Ivanov und A. A. Tuzhilin) Vestnik Moskov. Univ. Ser. I. Mat. Mech., 3(2002), 22-28
  • Steiner's Problem in Double Trees. (zusammen mit A. Dress und W. Fitch) Applied Mathematics Letters, 15(2002), no. 7, 855-860
  • A monoton iterative procedure to approximate trees of minimal length in metric spaces. Nonlinear Analysis, 47(2001), part 4, 2817-2828
  • The Vertex Degrees of Minimum Spanning Trees. Eurpean Journal of Operational Research, 125(2000), 278-282
  • The Steiner Ratio of finite-dimensional LP-spaces. (zusammen mit J. Albrecht) Advances of Steiner Trees, Eds. D. Z. Du, J. M. Smith and J. H. Rubinstein, Kluwer Acadamic Publishers, (2000), 1-13
  • The Steiner ratio for Riemannian manifolds. (Russian) (zusammen mit A. O. Ivanov und A. A. Tuzhilin) Uspekhi Mat. Nauk, 55 (2000), no 6., 139-140; English translation in Russian Math. Surveys.
  • k-Steiner-minimal-trees in metric spaces. Discrete Mathematics, 208/209 (1999), 119-124
  • The Steiner Ratio of L2kd. Discrete Applied Mathematics, 95 (1999), 217-221
  • Using Dvoretzky's Theorem in Network Design. Journal of Geometry, 65 (1999), 7-8
  • Steiner Minimal Trees in Lp2. (zusammen mit J. Linhart) Discrete Mathematics, 155 (1996), 39-48
  • A graph-theoretical method to approximate Steiner Minimal Trees in Banach Minkowski planes. Journal of Geometry, 53 (1995), 7-8
  • The Vertex-Degrees of Steiner Minimal Trees in Banach-Minkowski Spaces. Geombinatorics, 3 (1994), 75-82
  • Steiner Minimal Trees Problem in Lp2. Ann. Discrete Mathematics, 51 (1992), 59-62
  • The 1-Steiner-Minimal-Tree-Problem in Minkowski-Spaces. Optimization, 22 (1991), 291-296
  • The Fermat-Steiner-Weber-Problem in Minkowski-Spaces. Optimization, 19 (1988), 485-489

Contributions to books

  • The Steiner-Ratio in Banach-Minkowski-Planes - A survey. Handbook of Combinatorial Optimization, Supplement Volume B, eds D. Z. Du, P. M. Pardalos, Springer, New York, 2005, 55-81
  • Network Design Problems. Encyklopedia of Optimization, eds C. A. Floudas and P. M. Pardalos, Kluwer Academic Publishers, 2001 vol. IV, 1-7
  • The Steiner-Ratio of Lp-planes. (zusammen mit J. Albrecht) Handbook of Combinatorial Optimization, Supplement Volume A, eds. D. Z. Du, P. M. Pardalos, Kluwer Acadamic Publishers, 1999, 573-590
  • The Steiner-Ratio in Banach-Minkowski-Planes. Contemporary Methods in Graph Theory, ed. R. Bodendieck, Mannheim, 1990, 231-247
  • The Vertex-Degrees of Steiner-Minimal-Trees in Minkowski-Planes. Topics in Combinatorics and Graph Theory, eds. R. Bodendieck and R. Henn, Heidelberg, 1990, 201-206

Conference Proceedings

  • The Steiner-Ratio of Banach Spaces. (zusammen mit S. Reiser) Proceedings of the 16th Australasien Workshop on Combinatorial Algorithms (AWOCA 2005) 2005, 77-84
  • The Steiner ratio of three-dimensional Lp-spaces is essentially greater than 0.5. (zusammen mit J. Albrecht) Congressus Numeratium, 153 (2001), 179-185
  • The Steiner Ratio of Lp3. (zusammen mit J. Albrecht) Generalized Convexity and Generalized Monotonicity, eds. N. Hadjisavvas, J. E. Martinez-Legaz, J. P. Penot, Lecture Notes in Economics and Mathematical Systems, 502 (2001), 73-87
  • The Steiner-Ratio of Lp-planes. (zusammen mit J. Albrecht) Approximation and Complexity in Numerical Optimization, Nonconvex Optimization and its Applications 42, Kluwer Acadamic Publishers, 2000, 17-30
  • The Steiner Ratio of finite-dimensional Lp-spaces. Charlemagne and his Heritage - 1200 Years of Civilization and Science in Europe; ed. P. L. Butzer, H. Th. Jongen, W. Oberschelp; vol. 2 - Mathematical Arts; Brepols, 1998, 353-360
  • Using Hadwinger Numbers in Network Design. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 40 (1998), Network Design: Connectivity and Facilities Location, eds. P. Pardalos and D. Z. Du, 59-78
  • A graph-theoretical method to approximate Steiner-Minimal-Trees in Banach-Minkowski-Planes. Lecture Notes in Operations Research, 1, ISORA'95, eds. D. Z. Du, X. S. Zhang, K. Cheng, World Publishing Corporation, Beijing, 1995, 213-220
  • Methods to Construct Shortest Trees in Banach-Minkowski Planes. Operations Research Proceedings 1994, Springer 1995, 329-334
  • 1-Steiner-Minimal-Trees in Metric Spaces. Congressus Numerantium, 98 (1993), 39-49
  • The Steiner Minimal Trees Problem in Lp2. Proceedings of the Fourth Czechoslovak Symposium on Combinatorics, Graphs and Complexity, Prachatice, 1990, Ann. Discrete Math., 51 (1992), 59-62