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Godfried Toussaint
Godfried T. Toussaint is a Professor of Computer Science and the Head of the Computer Science Program at New York University Abu Dhabi (NYUAD)〔(New York University Abu Dhabi )〕 in Abu Dhabi, United Arab Emirates. He does research on various aspects of computational geometry, discrete geometry, and their applications: pattern recognition (k-nearest neighbor algorithm, cluster analysis), motion planning, visualization (computer graphics), knot theory (stuck unknot problem), linkage (mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality (unimodal function), and others. Other interests include meander (art), compass and straightedge constructions, instance-based learning, music information retrieval, and computational music theory.〔(G. Toussaint profile ) at McGill University〕
He is a co-founder of the Annual ACM Symposium on Computational Geometry, and the Annual Canadian Conference on Computational Geometry.
Along with Selim Akl, he is an author and namesake of the efficient "Akl–Toussaint algorithm" for the construction of the convex hull of a planar point set. This algorithm exhibits a computational complexity with expected value linear in the size of the input.〔Selim G. Akl and Godfried T. Toussaint, "A fast convex hull algorithm," ''Information Processing Letters'', Vol. 7, August 1978, pp. 219-222.〕 In 1980 he introduced the relative neighborhood graph (RNG) to the fields of pattern recognition and machine learning, and showed that it contained the minimum spanning tree, and was a subgraph of the Delaunay triangulation. Three other well known proximity graphs are the nearest neighbor graph, the Urquhart graph, and the Gabriel graph. The first is contained in the minimum spanning tree, and the Urquhart graph contains the RNG, and is contained in the Delaunay triangulation. Since all these graphs are nested together they are referred to as the Toussaint hierarchy.〔A. Adamatzky, "Developing proximity graphs by physarum polycephalum : Does the plasmodium follow the Toussaint hierarchy," ''Parallel Processing Letters'',Vol. 19, No. 1, 2009, pp. 105-127.〕
==Mathematical research in music==
He recently spent a year in the Music Department at Harvard University doing research on musical similarity, a branch of music cognition. Since 2005 he has also been a researcher in the Centre for Interdisciplinary Research in Music Media and Technology in the Schulich School of Music at McGill University. He applies computational geometric and discrete mathematics methods to the analysis of symbolically represented music in general, and rhythm in particular. In 2004 he discovered that the Euclidean algorithm for computing the greatest common divisor of two numbers implicitly generates almost all the most important traditional rhythms of the world.〔G. T. Toussaint, ''"(The Euclidean algorithm generates traditional musical rhythms )"'', ''Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science'', Banff, Alberta, Canada, July 31 to August 3, 2005, pp. 47–56.〕 His application of mathematical methods for tracing the roots of Flamenco music were the focus of two Canadian television programs.〔("Flamenco Forensics" ), ''McGill Reporter, January 26, 2006.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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