کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6875476 1441957 2018 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the complexity of an expanded Tarski's fixed point problem under the componentwise ordering
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
On the complexity of an expanded Tarski's fixed point problem under the componentwise ordering
چکیده انگلیسی
Let Π be a finite lattice of integer points in a box of Rn and f an increasing mapping in terms of the componentwise ordering from Π to itself. The well-known Tarski's fixed point theorem asserts that f has a fixed point in Π. A simple expansion of f from Π to a larger lattice C of integer points in a box of Rn yields that the smallest point in C is always a fixed point of f (an expanded Tarski's fixed point problem). By introducing an integer labeling rule and applying a cubic triangulation of the Euclidean space, we prove in this paper that the expanded Tarski's fixed point problem is in the class PPA when f is given as an oracle. It is shown in this paper that Nash equilibria of a bimatrix game can be reformulated as fixed points different from the smallest point in C of an increasing mapping from C to itself. This implies that the expanded Tarski's fixed point problem has at least the same complexity as that of the Nash equilibrium problem. As a byproduct, we also present a homotopy-like simplicial method to compute a Tarski fixed point of f. The method starts from an arbitrary lattice point and follows a finite simplicial path to a fixed point of f.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Theoretical Computer Science - Volume 732, 7 July 2018, Pages 26-45
نویسندگان
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