Victor Klee

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Victor Klee is affiliated with the following schools: University of Virginia, University of Washington

Victor Klee's AcademicInfluence.com Rankings

Victor Klee

Mathematics

#497

World Rank

#972

Historical Rank

#224

USA Rank

Measure Theory

#302

World Rank

#464

Historical Rank

#132

USA Rank

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Mathematics

Why Is Victor Klee Influential?

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According to Wikipedia, Victor LaRue Klee, Jr. was a mathematician specialising in convex sets, functional analysis, analysis of algorithms, optimization, and combinatorics. He spent almost his entire career at the University of Washington in Seattle.

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Victor Klee's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

HOW GOOD IS THE SIMPLEX ALGORITHM (1970) (1054)
Helly's theorem and its relatives (1963) (521)
Combinatorial Geometry in the Plane (1964) (221)
Old And New Unsolved Problems In Plane Geometry And Number Theory (1991) (194)
Some topological properties of convex sets (1955) (188)
Convex bodies and periodic homeomorphisms in Hilbert space (1953) (162)
A Combinatorial Analogue of Poincaré's Duality Theorem (1964) (162)
On the Complexity of some Basic Problems in Computational Convexity: II. Volume and mixed volumes (1994) (156)
Combinatorial and graph-theoretical problems in linear algebra (1993) (146)
Some new results on smoothness and rotundity in normed linear spaces (1959) (145)
Some characterizations of convex polyhedra (1959) (142)
Thed-step conjecture for polyhedra of dimensiond<6 (1967) (141)
The d-Step Conjecture and Its Relatives (1987) (138)
On the complexity ofd- dimensional Voronoi diagrams (1979) (123)
Shellings of Spheres and Polytopes. (1974) (117)
Convexity of Chebyshev sets (1961) (108)
Inner and outerj-radii of convex bodies in finite-dimensional normed spaces (1992) (105)
Extremal structure of convex sets. II (1958) (105)
Separation properties of convex cones (1955) (104)
When is a Matrix Sign Stable? (1977) (104)
On the complexity of some basic problems in computational convexity: I. Containment problems (1994) (101)
Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces (1993) (97)
FACETS AND VERTICES OF TRANSPORTATION POLYTOPES (1967) (95)
Polyhedral sections of convex bodies (1960) (87)
Leray-Schauder theory without local convexity (1960) (84)
Shrinkable neighborhoods in Hausdorff linear spaces (1960) (78)
Which Spheres are Shellable (1978) (76)
Invariant metrics in groups (solution of a problem of Banach) (1952) (74)
On the Number of Vertices of a Convex Polytope (1964) (73)
What Are the Intersection Graphs of Arcs in a Circle (1969) (71)
Finding the Smallest Triangles Containing a Given Convex Polygon (1985) (70)
The Euler Characteristic in Combinatorial Geometry (1963) (67)
Largest j-simplices in d-cubes: Some relatives of the hadamard maximum determinant problem (1996) (66)
Convex functions and upper semi-continuous collections (1952) (66)
On Certain Intersection Properties of Convex Sets (1951) (62)
Experimental designs through level reduction of the d-dimensional cuboctahedron (1972) (62)
The Critical Set of a Convex Body (1953) (61)
Circumspheres and Inner Products. (1960) (60)
Optimization of globally convex functions (1989) (59)
Computational complexity of norm-maximization (1990) (59)
Some semicontinuity theorems for convex polytopes and cell-complexes (1964) (59)
Can the Measure of ∪ n 1 [ a i , b i ] be Computed in Less Than O(n logn) Steps? (1977) (58)
CONVEX FUNCTIONS ON CONVEX POLYTOPES (1968) (55)
Paths on polyhedra. II. (1964) (55)
A NOTE ON TOPOLOGICAL PROPERTIES OF NORMED LINEAR SPACES (1956) (52)
Deterministic and randomized polynomial-time approximation of radii (2001) (51)
Diameters of Random Graphs (1981) (49)
SEPARATION AND SUPPORT PROPERTIES OF CONVEX SETS: A SURVEY. (1969) (49)
The structure of semispaces (1956) (46)
Qualitative stability of linear systems (1987) (45)
What is the Expected Volume of a Simplex Whose Vertices are Chosen at Random from a Given Convex Body (1969) (45)
Paths on Polyhedra. I (1965) (45)
Polytope pairs and their relationship to linear programming (1974) (44)
Diameters of Polyhedral Graphs (1964) (44)
Many Polytopes Meeting the Conjectured Hirsch Bound (1998) (44)
Continuous Convex Sets. (1959) (43)
Mappings into normed linear spaces (1960) (42)
Is Every Polygonal Region Illuminable from Some Point (1969) (42)
A proof of the strict monotone 4-step conjecture (1998) (42)
The generation of convex hulls (1963) (41)
The finite topology of a linear space (1963) (41)
Some Unsolved Problems in Plane Geometry (1979) (38)
On the Borelian and Projective Types of Linear Subspaces. (1958) (38)
Stability of the fixed-point property (1961) (37)
What is the Maximum Length of a d-Dimensional Snake? (1970) (37)
Maximal separation theorems for convex sets (1968) (37)
Approximation of diameters: randomization doesn't help (1998) (35)
CONVEX POLYTOPES AND LINEAR PROGRAMMING. (1964) (35)
Dispersed Chebyshev sets and coverings by balls (1981) (34)
Combinatorial Optimization: What is the State of the Art (1980) (34)
Convex and Linear Orientations of Polytopal Graphs (2000) (32)
A Representation of 2-dimensional Pseudomanifolds and its use in the Design of a Linear-Time Shelling Algorithm (1978) (32)
A class of linear programming problems requiring a large number of iterations (1965) (31)
Largest j-Simplices in n-Polytopes (1994) (31)
A Method for Constructing Circuit Codes (1967) (30)
Lengths of snakes in boxes (1967) (28)
Linear algorithms for testing the sign stability of a matrix and for findingZ-maximum matchings in acyclic graphs (1977) (28)
Every non-normable Frechet space is homeomorphic with all of its closed convex bodies (1966) (28)
Convex polytopes and related complexes (1996) (28)
Largestj-simplices inn-polytopes (1995) (27)
A Characterization of Convex Sets (1949) (27)
Polytope Projection and Projection Polytopes (1996) (27)
Mathematical Programming and Convex Geometry (1993) (27)
THE GREEDY ALGORITHM FOR FINITARY AND COFINITARY MATROIDS (1969) (24)
Exotic topologies for linear spaces (1962) (24)
Two topological properties of topological linear spaces (1964) (24)
Cross-Positive Matrices Revisited (1995) (23)
Basic properties of evenly convex sets (2007) (21)
QUALITATIVE MATRICES: STRONG SIGN-SOLVABILITY AND WEAK SATISFIABILITY (1981) (20)
A Generalization of Euler's φ-Function (1948) (20)
Computational Convexity (1996) (20)
EXPOSED POINTS OF CONVEX SETS (1966) (20)
Semicontinuity of the face-function of a convex set (1971) (19)
Extremal structure of convex sets (1957) (19)
Recursive structure of S-matrices and an O(m2) algorithm for recognizing strong sign solvability (1987) (19)
Invariant extension of linear functionals (1954) (19)
On a conjecture of Carmichael (1947) (19)
A characterization of reflexivity by the lattice of closed subspaces (1954) (18)
THE USE OF CIRCUIT CODES IN ANALOG-TO-DIGITAL CONVERSION, (1970) (18)
Common secants for plane convex sets (1954) (17)
Leray-Schauder theory without local convexity (1960) (17)
Asymptotes and Projections of Convex Sets. (1960) (16)
A qualitative analysis of I (1988) (16)
On the 0-1 Maximization of Positive Definite Quadratic Forms (1989) (16)
Inapproximability of some Geometric and Quadratic Optimization Problems (2000) (16)
Unsolved Problems in Intuitive Geometry (1960) (16)
Minimum Graphs of Specified Diameter, Connectivity and Valence. I (1975) (16)
On a Question of Bishop and Phelps (1963) (15)
Strict separation of convex sets (1956) (14)
Classification and enumeration of minimum (d, 1, 3)-graphs and minimum (d, 2, 3)-graphs (1977) (14)
Can a Plane Convex Body have Two Equichordal Points (1969) (14)
Geometry of the Gass-Saaty parametric cost LP algorithm (1990) (14)
Convex Set (1971) (13)
Shapes of the Future. (1971) (13)
Heights of convex polytopes (1965) (13)
Counterexamples to the Strong d -Step Conjecture for d≥5 (1998) (13)
Common supports as fixed points (1996) (12)
INTERSECTION THEOREMS FOR POSITIVE SETS (1969) (12)
Can the Measure of be Computed in Less than O(n log n) Steps (1977) (12)
On a conjecture of lindenstrauss (1963) (12)
Can Nine Tetrahedra Form a Neighboring Family (1969) (11)
Limits of starshaped sets (1987) (11)
Is a Body Spherical if its HA-Measurements are Constant? (1969) (11)
Classification and enumeration of minimum (d, 3, 3)-graphs for odd d (1980) (11)
On a theorem of Dubins (1963) (10)
Can the Boundary of a d-Dimensional Convex Body Contain Segments in all Directions? (1969) (10)
Appollonius Revisited: Supporting Spheres for Sundered Systems (1997) (10)
Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces (1996) (10)
Tiling with smooth and rotund tiles (1986) (10)
A comparison of primal and dual methods of linear programming (1966) (9)
Sign-Patterns and Stability (1989) (9)
Characterizations of a Class of Convex Sets. (1967) (9)
Monthly Research Problems, 1969–71 (1971) (9)
Shapes of the future - some unsolved problems in high-dimensional intuitive geometry (1999) (9)
Two renorming constructions related to a question of Anselone (1969) (9)
Extreme points of convex sets without completeness of the Scalar field (1964) (8)
Locally countable plump tilings are flat (1987) (8)
The Proportion of Labelled Bipartite Graphs which are Connected (1981) (8)
Asymptotes of Convex Bodies. (1967) (8)
A Note on Extreme Points (1955) (8)
Convexity and Optimization in Finite Dimension (Josef Stoer and Christoph Witzgall) (1972) (7)
A D-pseudomanifold with Fo Vertices Has at Least Dfo-(d-1 )(d+2) D-simplices (2004) (7)
Good and Bad Radii of Convex Polygons (1991) (7)
Which generalized prisms admit H-circuits? (1972) (7)
A note on certain function spaces (1957) (7)
Convex Polyhedra and Mathematical Programming. (1974) (7)
Diameters of random bipartite graphs (1984) (7)
Another generalization of Carathéodory's theorem (1980) (7)
Summability in $ł(p_{1},p_{2},...)$ spaces (1965) (7)
Some Proximate Concepts in Topology. (1973) (7)
Impressions of Mathematical Education in the People's Republic of China (1977) (7)
Some Characterizations of Compactness (1951) (7)
Inner diagonals of convex polytopes (1999) (7)
The Diameter of Almost All Bipartite Graphs. (1980) (6)
A d-Pseudomanifold with f(sub 0) Vertices Has at Least df(sub 0)-(d-1)(d+2) d-Simplices. (1975) (6)
Adjoints of projective transformations and face-figures of convex polytopes (1978) (6)
On a Theorem of Bela Sz.-Nagy (1953) (6)
Minimum graphs of specified diameter, connectivity and valence. II (1989) (6)
Oracle-polynomial-time approximation of largest simplices in convex bodies (2000) (6)
Solution of a Problem of E. M. Wright on Convex Functions (1956) (6)
Linear Programming and Extensions. George B. Dantzig. Princeton University Press, Princeton, N.J., 1963. xviii + 625 pp. Illus. $11.50 (1964) (6)
Deciding uniqueness in norm maximization (1992) (5)
A String Algorithm for Shortest Path in Directed Networks (1964) (5)
Polytope Containment and Determination by Linear Probes (1995) (5)
Iteration of the "lin" operation for convex sets (1956) (5)
A theorem on convex kernels (1965) (5)
HOMOGENEITY OF INFINITE-DIMENSIONAL PARALLELOTOPES* (1957) (5)
Is there an n for which φ(x)=n has a Unique Solution? (1969) (5)
Fixed-Point Sets of Periodic Homeomorphisms of Hilbert Space (1956) (4)
Sharper approximation of extreme points by far points (1993) (4)
How Many Steps (1980) (4)
Every Simple Closed Curve in E3 is Unknotted in E4 (1964) (4)
The November meeting in Los Angeles (1956) (4)
Problem in Barycentric Coordinates (1965) (4)
The Connectedness Game and the c-Complexity of Certain Graphs (1977) (4)
Spira's Theorems on Complete Linear Proofs of Systems of Linear Inequalities. (1975) (4)
Decomposition Theorems for Conditional Sign-Solvability and Sign-Solvability of General Systems (2000) (4)
Topological equivalence of a Banach space with its unit cell (1961) (4)
Use of Floyd's Algorithm to Find Shortest Restricted Paths. (1979) (3)
Must a Compact Endset Have Measure Zero (1970) (3)
Connectedness in topological linear spaces (1964) (3)
Unique reducibility of subsets of commutative topological groups and semigroups. (1975) (3)
On the Equation π(x) = 2m (1946) (3)
A note on convex cones and constraint qualifications in infinite-dimensional vector spaces (1982) (3)
Uniform properties of collections of convex bodies (1991) (3)
Topological structure of infinite-dimensional linear spaces: the classification problem (1963) (2)
Which Isoperimetric Ratios are Bounded (1970) (2)
On the recognition of S-systems (1993) (2)
Unions of increasing and intersections of decreasing sequences of convex sets (1972) (2)
Inspheres and inner products (1986) (2)
Utility functions and the ‘lin’ operation for convex sets (1964) (2)
Can All Convex Borel Sets Be Generated in a Borelian Manner Within the Realm of Convexity (1969) (2)
Decomposition of an Infinite-Dimensional Linear System into Ubiquitous Convex Sets (1950) (2)
On a method of mapping due to Kadeč and Bernstein (1957) (2)
The April meeting in Berkeley (1957) (2)
On the limited power of linear probes and other optimization oracles (1990) (2)
Random Bipartite Graphs: Connectedness, Isolated Nodes, Diameters. (1979) (2)
Separation by Hyperplanes in Finite-Dimensional Vector Spaces Over Archimedean Ordered Fields (1997) (2)
On metric independence and linear independence (1955) (2)
Contributions to Functional Analysis (1966) (1)
Polytopal Complexes and Their Relatives (1987) (1)
The Plane Covered by Disks: 10440 (1999) (1)
Ratio-sequences of chains in connected metric spaces (1975) (1)
A SURPRISING BUT EASILY PROVED GEOMETRIC DECOMPOSITION THEOREM (1998) (1)
On a lemma of fullerton and braunschweiger (1969) (1)
Behavior of linear forms on extreme points (1968) (1)
Idempotency of the hull-formation Hγ (1963) (1)
A question of Katětov concerning the Hilbert parallelotope (1961) (1)
A conjecture on weak compactness (1962) (1)
The April meeting in Monterey (1956) (1)
COMBINATORIAL OPTIMIZATION: WHAT IS THE STATE OF THE ART? (1979) (1)
Convex Analysis (R. Tyrrell Rockafellar) (1971) (1)
An example in the theory of topological linear spaces (1956) (1)
A linearly compact convex set dense in every vector topology (1977) (1)
Linear algebra, polytopes, and the hirsch conjecture (1996) (1)
On a problem of Banach (1958) (1)
On a Problem of Erdos (1949) (1)
Rearrangements of series of vectors (1963) (1)
Corrections: Some Remarks on Euler's Totient (1948) (1)
THE JUNE MEETING IN PORTLAND The five hundred fourth meeting of the American Mathematical (2007) (0)
A Connectedness Game, c-Complexity of Graphs, and a Linear-Time Shelling Algorithm. (1975) (0)
Review: F. A. Valentine, Convex sets (1969) (0)
NSF Budget Changes Threaten CUPM Effort (1971) (0)
Title Strict convexity and smoothness of normed spaces (0)
Correction to "Summability in $ł(p_{1},p_{2},...)$ spaces" Studia Mathematica 25 (1965), p. 277-280) (1969) (0)
COMMON SECANTS FOR PLANE CONVEX SETS1 (2010) (0)
SOME UNSOLVED PROBLEMS CONCERNING CONVEX BODIES (1969) (0)
SEPARATION PROPERTIES OF CONVEX CONES1 (2010) (0)
In a remarkable paper, Bishop and Phelps (1) settle several important questions concerning supporting hyperplanes of convex sets in Banach spaces. In particular, they show that if C is a closed convex subset of a Banach space (2016) (0)
Convex Functions (A. Wayne Roberts and Dale E. Varberg) (1976) (0)
Problems for Solution: E736-E740 (1946) (0)
SOME TOPOLOGICAL PROPERTIES OF CONVEX SETS(1) (2016) (0)
Problems for Solution: E1048,E1076-E1080 (1953) (0)
A GEOMETRIC PROOF OF RYLL-NARDZEWSKI'S FIXED POINT THEOREM BY I. NAMIOKA AND E. ASPLUND (2007) (0)
Computations of Optimal Experimental Designs of Estimation of Linear Forms. (1971) (0)
PATHS IN POLYTOPES: A SURVEY, (1966) (0)
Correction (1983) (0)
The June meeting in Vancouver (1955) (0)
36 COMPUTATIONAL CONVEXITY (2016) (0)
Efficient Width-Computation of high-dimensional point sets (1998) (0)
Problems for Solution: 4738-4742 (1957) (0)
Finding Largest Simplices (Preliminary Report) (1992) (0)
PROBLEM SIZE IN LINEAR PROGRAMMING (1966) (0)
A Linear Matching Algorithm for Acyclic Graphs. (1976) (0)
The June meeting in Pullman (1957) (0)
Banach Spaces and Hilbert Spaces (1986) (0)
External Tangents and Closedness of Cone + Subspace (1994) (0)
Guest Editors' Foreword (2000) (0)
Letter from Victor Klee to Joshua Lederberg (1965) (0)
A Note on Fermat's Congruence (1949) (0)
SOME TOPOLOGICAL PROPERTIES OF CONVEX SETSO (2010) (0)
The April meeting in Stanford (1958) (0)
A Comment on Floyd's Algorithm for Shortest Chains. (1973) (0)
UNCLASSIFIED AD DEFENSE DOCUMENTATION CENTER FOR SCIENTIFIC AND TECHNICAL INFORMATION CAMERON STATION (2009) (0)
On Completing a Determinant (1947) (0)
An O(n squared) Algorithm for Testing the Sign Stability of an n x n Matrix. (1975) (0)
MORE DISTANT THAN THE ANTIPODES (2007) (0)
Problems for Solution: 4310-4314 (1948) (0)
A Combinatorial Analogue of (1963) (0)
Problems for Solution: 4350-4354 (1949) (0)
The use of research problems in high school geometry (1971) (0)
Archimedean levels, semispaces, and majorization of convex cones (1993) (0)
Dantzig's Simplex Method: Linear Programming and Extensions . George B. Dantzig. Princeton University Press, Princeton, N.J., 1963. xviii + 625 pp. Illus. $11.50. (1964) (0)
Two examples in the theory of topological linear spaces (1965) (0)
The November meeting in Pasadena (1957) (0)
On a Question of Colin Clark Concerning Three Properties of Convex Sets(1) (1972) (0)
The Secretary announced the election of the following ninety-two persons to ordinary membership in the Society (2007) (0)
Combinatorial Mathematics. Herbert John Ryser. Published for the Mathematical Association of America by Wiley, New York, 1963. xiv + 154 pp. Illus. $4 (1963) (0)
The summer meeting in Seattle (1956) (0)
Problems for Solution: 4899-4904 (1960) (0)

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