V ictor L. Klee passed away on August 17, 2007, in Lakewood, Ohio. Born in San Francisco in 1925, he received his Ph.D. in mathematics from the University of Virginia in 1949. In 1953 he moved to the University of Washington in Seattle, where he was a faculty member for 54 years. Klee specialized in convex sets, functional analysis, analysis of algorithms, optimization, and combinatorics, writi...

Kitahara and Mizuno [3] get upper bounds for the maximum number of different basic feasible solutions generated by Dantzig’s simplex method. In this paper, we obtain lower bounds of the maximum number. Part of the results in this paper are shown in Kitahara and Mizuno [4] as a quick report without proof. They present a simple variant of Klee-Minty’s LP and get a lower bound. In this paper, we e...

By introducing redundant Klee-Minty examples, we have previously shown that the central path can be bent along the edges of the Klee-Minty cubes, thus having 2n − 2 sharp turns in dimension n. In those constructions the redundant hyperplanes were placed parallel with the facets active at the optimal solution. In this paper we present a simpler and more powerful construction, where the redundant...

We show that in all dimensions d ≥ 3, there exists an asymmetric convex body of revolution all of whose maximal hyperplane sections have the same volume. This gives the negative answer to the question posed by V. Klee in 1969.

Software bugs are a well-known source of security vulnerabilities. One technique for finding bugs, symbolic execution, considers all possible inputs to a program but suffers from scalability limitations. This paper uses a variant, under-constrained symbolic execution, that improves scalability by directly checking individual functions, rather than whole programs. We present UC-KLEE, a novel, sc...