Finding a Simple Polytope from Its Graph in Polynomial Time
نویسندگان
چکیده
منابع مشابه
Finding a Simple Polytope from Its Graph in Polynomial Time
We show that one can compute the combinatorial facets of a simple polytope from its graph in polynomial time. Our proof relies on a primal-dual characterization (by Joswig, Kaibel and Korner) and a linear program, with an exponential number of constraints, which can be used to construct the solution and can be solved in polynomial time. We show that this allows one to characterize the face latt...
متن کاملFinding Short Cycles in an Embedded Graph in Polynomial Time
Let C1 be the set of fundamental cycles of breadth-first-search trees in a graph G and C2 the set of the sums of two cycles in C1. Then we show that (1).C = C1 ⋃ C2 contains a shortest Π-twosided cycle in a Π-embedded graph G.This implies the existence of a polynomially bounded algorithm to find a shortest Π−twosided cycle in an embedded graph and thus solves an open problem of Mohar and Thomas...
متن کاملFinding Relations in Polynomial Time
Given a set of m observations on n variables, an 0(mn) algorithm is proposed to find a basis of all affine relations between these variables satisfied by the observations. On a 25 variables example, this new algorithm is 130 000 times faster than the "all subsets" option for linear regression of the SAS package which is a non polynomial alternative. Extension to the cases where squares, ratios,...
متن کاملFinding a Maximum Cut of a Planar Graph in Polynomial Time
The problem of finding a maximum cut of an arbitrary graph is one of a list of 21 com-binatorial problems (Karp-Cook list). It is unknown whether or not there exist algorithms operating in polynomial bounded time for any of these problems. It has been shown that existence for one implies existence for all. In this paper we deal with a special case of the maximum cut problem. By requiring the gr...
متن کاملFinding Regular Simple Paths in Graph Databases
We consider the following problem: given a labelled directed graph G and a regular expression R, find all pairs of nodes connected by a simple path such that the concatenation of the labels along the path satisfies R. The problem is motivated by the observation that many recursive queries can be expressed in this form, and by the implementation of a query language, G+, based on this observation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9121-7