Approximation Problems Categories

abstract NP-hard optimization problem, in a general sense. From the observation that, intuitively, there are many connections among categorical concepts and structural complexity notions, we started defining two categories: the OPTS category of polynomial time soluble optimization problems, which morphisms are reductions, and the OPT category of optimization problems, having approximationpreserving reductions as morphisms. The study of approximation implies to create means of comparing optimization problems. The basic idea of approximation by models is a recurrent one in mathematics and in this direction a comparison mechanism between the OPTS and OPT categories has been introduced in [5]. In order to establish a formal ground for the study of the approximation properties of optimization problems, a system approximation to each optimization problem is constructed, based on categorical shape theory. In so doing, we were very much inspired in previous works ∗This work is partially sup...

• Type: Conference
• Year: 2005
• Where: EUROCAST
• Authors: Liara Aparecida dos Santos Leal, Dalcidio Moraes Claudio, Laira Vieira Toscani, Paulo Blauth Menezes
• Keywords: Approximation, EUROCAST 2005, NP-hard Optimization Problem, Optimization Problems