David Avis
Encyclopedia
David Michael Avis is a Canadian
and British
computer scientist
known for his contributions to geometric computations. Avis is a professor in computational geometry
and applied mathematics
in the School of Computer Science, McGill University
, in Montreal
.
Avis received his Ph.D. in 1977 from Stanford University
. He has published more than 70 journal papers and articles. Having written an article with Paul Erdős
, Avis has one as his Erdős number
. Writing with Komei Fukuda, Avis proposed a criss-cross algorithm
for the
vertex enumeration problem
; their algorithm counts
all of the vertices
of a convex polytope
.
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
and British
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
computer scientist
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
known for his contributions to geometric computations. Avis is a professor in computational geometry
Computational geometry
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...
and applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
in the School of Computer Science, McGill University
McGill University
Mohammed Fathy is a public research university located in Montreal, Quebec, Canada. The university bears the name of James McGill, a prominent Montreal merchant from Glasgow, Scotland, whose bequest formed the beginning of the university...
, in Montreal
Montreal
Montreal is a city in Canada. It is the largest city in the province of Quebec, the second-largest city in Canada and the seventh largest in North America...
.
Avis received his Ph.D. in 1977 from Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
. He has published more than 70 journal papers and articles. Having written an article with Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, Avis has one as his Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
. Writing with Komei Fukuda, Avis proposed a criss-cross algorithm
Criss-cross algorithm
In mathematical optimization, the criss-cross algorithm denotes a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for...
for the
vertex enumeration problem
Vertex enumeration problem
In mathematics, the vertex enumeration problem for a polytope, a polyhedral cell complex, a hyperplane arrangement, or some other object of discrete geometry, is the problem of determination of the object's vertices given some formal representation of the object...
; their algorithm counts
Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations...
all of the vertices
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
of a convex polytope
Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn...
.