In a paper presented at a 1996 conference, Holt and Klee introduced a set of necessary conditions for an orientation of the graph of a d-polytope to be induced by a realization into Rn and linear functional on that space. In general, it is an open question to decide whether for a polytope P every orientation of its graph satisfying these conditions can in fact be realized in this fashion; two n...

In Euclidean spaces, the geometric notions of nearest-points map, farthestpoints map, Chebyshev set, Klee set, and Chebyshev center are well known and well understood. Since early works going back to the 1930s, tremendous theoretical progress has been made, mostly by extending classical results from Euclidean space to Banach space settings. In all these results, the distance between points is i...

The Klee-Quaife problem is finding the minimum order μ(d, c, v) of the (d, c, v) graph, which is a c-vertex connected v-regular graph with diameter d. Many authors contributed finding μ(d, c, v) and they also enumerated and classified the graphs in several cases. This problem is naturally extended to the case of digraphs. So we are interested in the extended Klee-Quaife problem. In this paper, ...

Some decades ago, V. Klee and G.-C.Rota introduced a lattice-theoretic analogue of the Euler characteristic, the celebrated topological invariant of polyhedra. In [1], using the Klee-Rota definition, we introduce the Euler characteristic of a formula in Gödel logic, the extension of intuitionistic logic via the prelinearity axiom. We then prove that the Euler characteristic of a formula over n ...

Linear programming (LP) is an important field of optimization. Even though, interior point methods are polynomial algorithms, many LP practical problems are solved more efficiently by the primal and dual revised simplex methods (RSM); however, RSM has a poor performance in hard LP problems (HLPP) as in the Klee-Minty Cubes problem. Among LP methods, the hybrid method known as Simplex-Genetic (S...

Abstract Symbiotic-Witch is a new tool for checking violation witnesses in the GraphML-based format used at SV-COMP since 2015. Roughly speaking, symbolically executes given program with Klee and simultaneously tracks set of nodes witness automaton can be in. Moreover, it reads return values nondeterministic functions specified uses them to prune symbolic execution. The confirmed if execution r...