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Discrete Mathematical Problems with Medical Applications
Edited by: Ding-Zhu Du, University of Minnesota, Minneapolis, MN, Panos M. Pardalos, University of Florida, Gainesville, FL, and Jie Wang, University of North Carolina, Greensboro, NC
A co-publication of the AMS and DIMACS.

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
2000; 219 pp; hardcover
Volume: 55
ISBN-10: 0-8218-2096-6
ISBN-13: 978-0-8218-2096-4
List Price: US$84
Member Price: US$67.20
Order Code: DIMACS/55
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This volume presents selected papers from a three-day workshop held during the DIMACS special years on Mathematical Support for Molecular Biology. Participants from the world over attended, giving the workshop an important international component.

The study of discrete mathematics and optimization with medical applications is emerging as an important new research area. Significant applications have been found in medical research, for example in radiosurgical treatment planning, virtual endoscopy, and more. This volume presents a substantive cross-section of active research topics ranging from medical imaging to human anatomy modeling, from gamma knife treatment planning to radiation therapy, and from epileptic seizures to DNA screening. This book is an up-to-date resource reflecting current research directions.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).


Graduate students and research mathematicians interested in computer science, discrete mathematics, and image processing.

Table of Contents

  • Y.-J. Lee, O. L. Mangasarian, and W. H. Wolberg -- Breast cancer survival and chemotherapy: A support vector machine analysis
  • P. Hall -- A model for learning human vascular anatomy
  • M. C. Ferris and D. M. Shepard -- Optimization of gamma knife radiosurgery
  • Q. J. Wu -- Sphere packing using morphological analysis
  • L. D. Iasemidis, D.-S. Shiau, J. C. Sackellares, and P. Pardalos -- Transition to epileptic seizures: Optimization
  • I. Nyström and Smedby -- Analysis of magnetic resonance angiography images using skeletonization and distance transforms
  • S. Bouix and K. Siddiqi -- Computing medial surfaces
  • A. Rangarajan and H. Chui -- A mixed variable optimization approach to non-rigid image registration
  • B. DasGupta, X. He, T. Jiang, M. Li, J. Tromp, and L. Zhang -- On computing the nearest neighbor interchange distance
  • A. J. Macula, D. C. Torney, and P. A. Vilenkin -- Two-stage group testing for complexes in the presence of errors
  • L. Sheng, C. Wang, and P. Zhang -- On the perfectness of tagged probe interval graphs
  • S. E. Brossette and A. P. Sprague -- Frequent sets in the presence of clones: An example from medical surveillance
  • H. Q. Ngo and D.-Z. Du -- A survey on combinatorial group testing algorithms with applications to DNA Library Screening
  • Q. J. Wu, J. Wang, and C. H. Sibata -- Optimization problems in 3D conformal radiation therapy
  • A. Kuba, G. T. Herman, S. Matej, and A. Todd-Pokropek -- Medical applications of discrete tomography
  • J. K. Udupa -- A study of 3D imaging approaches in medicine
  • P. Hall -- Discrete mathematics in medical imaging: A personal view
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