Category theory for computing science
Category theory for computing science
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Identification and Recognition through Shape in Complex Systems
EUROCAST '95 Selection of Papers from the Fifth International Workshop on Computer Aided Systems Theory
Optimization Problems Categories
Computer Aided Systems Theory - EUROCAST 2001-Revised Papers
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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In this paper we continue along the same line of research started in earlier works, towards to providing a categorical view of structural complexity to optimization problems. The main aim is to provide a universal language for supporting formalisms to specify the hierarchy approximation system for an abstract NP-hard optimization problem. Categorical shape theory provides the mathematical framework to deal with approximation, enabling comparison of objects of interest and of models. In this context, tractable optimization problems are considered as a class of “models” or “prototypes” within a larger class of objects of interest – the intractable optimization problems class. Standard categorial constructions like universal objects, functors and adjunctions allow to formalize an approximation hierarchy system to optimization problems, besides characterizing NP-hard optimization problems as concrete universal objects.