Note on the computational complexity of j-radii of polytopes in n
نویسندگان
چکیده
We show that, for fixed dimension n, the approximation of inner and outer j-radii of polytopes in N", endowed with the Euclidean norm, is in P. Our method is based on the standard polynomial time algorithms for solving a system of polynomial inequalities over the reals in fixed dimension.
منابع مشابه
Reduction of Computational Complexity in Finite State Automata Explosion of Networked System Diagnosis (RESEARCH NOTE)
This research puts forward rough finite state automata which have been represented by two variants of BDD called ROBDD and ZBDD. The proposed structures have been used in networked system diagnosis and can overcome cominatorial explosion. In implementation the CUDD - Colorado University Decision Diagrams package is used. A mathematical proof for claimed complexity are provided which shows ZBDD ...
متن کاملRadii of Regular Polytopes
There are three types of regular polytopes which exist in every dimension d: regular simplices, (hyper-) cubes, and regular cross-polytopes. In this paper we investigate two pairs of inner and outer j-radii (rj, Rj) and (r̄j, R̄j) of these polytopes (inner and outer radii classes are almost always considered in pairs, such that for a 0-symmetric body K and its dual K the inner (outer) radii of K ...
متن کاملLinear Programming, the Simplex Algorithm and Simple Polytopes
In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
متن کاملConvex hulls of spheres and convex hulls of disjoint convex polytopes
Given a set Σ of spheres in E, with d ≥ 3 and d odd, having a constant number of m distinct radii ρ1, ρ2, . . . , ρm, we show that the worst-case combinatorial complexity of the convex hull of Σ is Θ( ∑ 1≤i6=j≤m nin ⌊ d 2 ⌋ j ), where ni is the number of spheres in Σ with radius ρi. To prove the lower bound, we construct a set of Θ(n1+n2) spheres in E , with d ≥ 3 odd, where ni spheres have rad...
متن کاملA note on the extension complexity of the knapsack polytope
We show that there are 0-1 and unbounded knapsack polytopes with super-polynomial extension complexity. More specifically, for each n ∈ N we exhibit 0-1 and unbounded knapsack polyhedra in dimension n with extension complexity Ω(2 p n).
متن کامل