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61.
Computing the minimal covering set 总被引:1,自引:0,他引:1
We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm draws upon a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set–the minimal upward covering set and the minimal downward covering set–unless P equals NP. Finally, we observe a strong relationship between von Neumann–Morgenstern stable sets and upward covering on the one hand, and the Banks set and downward covering on the other. 相似文献
62.
The overlay of 2≤m≤d minimization diagrams of n surfaces in ℝ
d
is isomorphic to a substructure of a suitably constructed minimization diagram of mn surfaces in ℝ
d+m−1. This elementary observation leads to a new bound on the complexity of the overlay of minimization diagrams of collections
of d-variate semi-algebraic surfaces, a tight bound on the complexity of the overlay of minimization diagrams of collections of
hyperplanes, and faster algorithms for constructing such overlays. Further algorithmic implications are discussed.
Work by V. Koltun was supported by NSF CAREER award CCF-0641402.
Work by M. Sharir was supported by NSF Grants CCR-00-98246 and CCF-05-14079, by a grant from the Israeli Academy of Sciences
for a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski Minerva Center for
Geometry at Tel Aviv University. 相似文献
63.
64.
65.
Zvi Drezner 《Mathematical Programming》1987,38(2):219-222
We present an exchange algorithm for the solution of minimax optimization problems involving convex functions. For a certain
class of functions, the complexity of this algorithm is shown to be either linear in the number of functions, or at least
squared in that number. 相似文献
66.
Isabel Oitavem 《Mathematical Logic Quarterly》2008,54(3):323-329
This paper gives an implicit characterization of the class of functions computable in polynomial space by deterministic Turing machines – PSPACE. It gives an inductive characterization of PSPACE with no ad‐hoc initial functions and with only one recursion scheme. The main novelty of this characterization is the use of pointers (also called path information) to reach PSPACE. The presence of the pointers in the recursion on notation scheme is the main difference between this characterization of PSPACE and the well‐known Bellantoni‐Cook characterization of the polytime functions – PTIME. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
67.
68.
本文对外代数上复杂度为2的不可分解循环Koszul模M的极小投射分解进行了分析,构造出了基映射对应的矩阵的一种标准形式,进而刻划出了其合冲ΩM的滤链结构. 相似文献
69.
S. V. Ivanov 《Geometriae Dedicata》2008,131(1):1-26
We study the computational complexity of basic decision problems of 3-dimensional topology, such as to determine whether a
triangulated 3-manifold is irreducible, prime, ∂-irreducible, or homeomorphic to a given 3-manifold M. For example, we prove that the problem to recognize whether a triangulated 3-manifold is homeomorphic to a 3-sphere, or
to a 2-sphere bundle over a circle, or to a real projective 3-space, or to a handlebody of genus g, is decidable in nondeterministic polynomial time (NP) of size of the triangulation. We also show that the problem to determine whether a triangulated orientable 3-manifold is
irreducible (or prime) is in PSPACE and whether it is ∂-irreducible is in coNP. The proofs improve and extend arguments of prior author’s article on the recognition problem for the 3-sphere.
相似文献
70.
This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities. 相似文献