## Discrete Mathematical Problems with Medical Applications: DIMACS Workshop Discrete Mathematical Problems with Medical Applications, December 8-10, 1999, DIMACS CenterDingzhu Du, Panos M. Pardalos, Jie Wang 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. |

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### Contents

A model for learning human vascular anatomy | 11 |

Optimization of gamma knife radiosurgery | 27 |

Sphere packing using morphological analysis | 45 |

Analysis of magnetic resonance angiography images using skeletonzation | 75 |

Computing medial surfaces | 91 |

A mixed variable optimization approach to nonrigid image registration | 105 |

On computing the nearest neighbor interchange distance | 125 |

Twostage group testing for complexes in the presence of errors | 145 |

On the perfectness of tagged probe interval graphs | 159 |

A survey on combinatorial group testing algorithms with applications | 171 |

Medical applications of discrete tomography | 195 |

Open Problems | 208 |

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algorithm analysis angiograms applications approach beam chemotherapy clone Computer Science constraints corresponding curve skeleton defined denote Discrete Mathematics discrete tomography distance transformation dose distribution dynamical E-mail address Editors epileptic seizures error exact cover example Figure frequent sets furcation fuzzy Gamma Knife geometry group testing integer internal edges iteration J. C. Sackellares k-complexes labels leaf labels Lemma Lyapunov exponents matching Mathematics Subject Classification matrix measure medial surface Medical Imaging minimize nn nn nni distance nni moves nni operations non-rigid nonlinear NP-complete O. L. Mangasarian objective function optimization outliers parameters patients phase space phylogenies points pooling design probe interval graph problem programming projections radiosurgery region representation row and column Section segmentation sequence simulated slices solution spatial mapping structure subgraph subset sulcal support vector machine tagged probe interval Theorem thin-plate spline topology treatment planning tree tumor values variables vasculature vessel fragments voxels warping

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Page i - Neil Immerman and Phokion G. Kolaitis. Editors. Descriptive Complexity and Finite Models 30 Sandeep N. Bhatt. Editor, Parallel Algorithms: Third DIMACS Implementation Challenge 29 Doron A. Peled, Vaughan R. Pratt. and Gerard J. Holzmann, Editors. Partial Order Methods in Verification 28 Larry Finkelstein and William M.