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Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
Harold Abelson is an American mathematician and computer scientist. He is a professor of computer science and engineering in the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology (MIT), a founding director of both Creative Commons and the Free Software Foundation, creator of the MIT App Inventor platform, and co-author of the widely-used textbook Structure and Interpretation of Computer Programs, sometimes also referred to as "the wizard book."
A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system of line segments with the points as endpoints, minimizing the total length of the segments. In it, any two points can reach each other along a path through the line segments. It can be found as the minimum spanning tree of a complete graph with the points as vertices and the Euclidean distances between points as edge weights.
In computational geometry, the Theta graph, or -graph, is a type of geometric spanner similar to a Yao graph. The basic method of construction involves partitioning the space around each vertex into a set of cones, which themselves partition the remaining vertices of the graph. Like Yao Graphs, a -graph contains at most one edge per cone; where they differ is how that edge is selected. Whereas Yao Graphs will select the nearest vertex according to the metric space of the graph, the -graph defines a fixed ray contained within each cone and selects the nearest neighbor with respect to orthogonal projections to that ray. The resulting graph exhibits several good spanner properties.
David Arthur Eppstein is an American computer scientist and mathematician. He is a distinguished professor of computer science at the University of California, Irvine. He is known for his work in computational geometry, graph algorithms, and recreational mathematics. In 2011, he was named an ACM Fellow.
A geometric spanner or a t-spanner graph or a t-spanner was initially introduced as a weighted graph over a set of points as its vertices for which there is a t-path between any pair of vertices for a fixed parameter t. A t-path is defined as a path through the graph with weight at most t times the spatial distance between its endpoints. The parameter t is called the stretch factor or dilation factor of the spanner.
Godfried Theodore Patrick Toussaint was a Canadian computer scientist, a professor of computer science, and the head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates. He is considered to be the father of computational geometry in Canada. He did research on various aspects of computational geometry, discrete geometry, and their applications: pattern recognition, motion planning, visualization, knot theory, linkage (mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality, and others. Other interests included meander (art), compass and straightedge constructions, instance-based learning, music information retrieval, and computational music theory.
Planarity is a 2005 puzzle computer game by John Tantalo, based on a concept by Mary Radcliffe at Western Michigan University. The name comes from the concept of planar graphs in graph theory; these are graphs that can be embedded in the Euclidean plane so that no edges intersect. By Fáry's theorem, if a graph is planar, it can be drawn without crossings so that all of its edges are straight line segments. In the planarity game, the player is presented with a circular layout of a planar graph, with all the vertices placed on a single circle and with many crossings. The goal for the player is to eliminate all of the crossings and construct a straight-line embedding of the graph by moving the vertices one by one into better positions.
Kurt Mehlhorn is a German theoretical computer scientist. He has been a vice president of the Max Planck Society and is director of the Max Planck Institute for Computer Science.
János Pach is a mathematician and computer scientist working in the fields of combinatorics and discrete and computational geometry.
Roberto Tamassia is an American Italian computer scientist, the Plastech Professor of Computer Science at Brown University, and served as the chair of the Brown Computer Science department from 2007 to 2014. His research specialty is in the design and analysis of algorithms for graph drawing, computational geometry, and computer security; he is also the author of several textbooks.
Jörg-Rüdiger Wolfgang Sack is a professor of computer science at Carleton University, where he is Chancellor's Professor. </ref> Sack received a master's degree from the University of Bonn in 1979 and a Ph.D. in 1984 from McGill University, under the supervision of Godfried Toussaint. He is co-editor-in-chief and executive editor of the journal Computational Geometry: Theory and Applications, co-editor of the Handbook of Computational Geometry, and co-editor of the proceedings of the biennial Algorithms and Data Structures Symposium (WADS). He was a co-founding editor-in-chief of the open access Journal of Spatial Information Science but is no longer an editor there. Sack's research interests include computational geometry, data structures and geographic information systems.
Emmerich (Emo) Welzl is a computer scientist known for his research in computational geometry. He is a professor in the Institute for Theoretical Computer Science at ETH Zurich in Switzerland.
Prosenjit K. "Jit" Bose is a Canadian mathematician and computer scientist who works at Carleton University as a professor in the School of Computer Science and associate dean of research and graduate studies for the Faculty of Science. His research concerns graph algorithms and computational geometry, including work on geometric spanners and geographic routing in wireless ad hoc networks.
Jorge Urrutia Galicia is a Mexican mathematician and computer scientist in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). His research primarily concerns discrete and computational geometry.
Ferran Hurtado Díaz was a Spanish mathematician and computer scientist known for his research in computational geometry.
Gautam Das is a computer scientist in the field of databases research. He is an ACM Fellow and IEEE Fellow.
David Ronald Wood is a Professor in the School of Mathematics at Monash University in Melbourne, Australia. His research area is discrete mathematics and theoretical computer science, especially structural graph theory, extremal graph theory, geometric graph theory, graph colouring, graph drawing, and combinatorial geometry.
References
- 1 2 3 Curriculum vitae (PDF), retrieved 2019-11-20
- ↑ Pat Morin at the Mathematics Genealogy Project
- ↑ "Editorial team", Journal of Computational Geometry, retrieved 2019-11-20
- ↑ "Open Data Structures: An Introduction", Open Textbook Library, retrieved 2019-11-20. Includes two book reviews.
