Structural properties of bounded relations with an application to NP optimization problems

Structural properties of bounded relations with an application to NP optimization problems

We introduce the notion bounded relation which comprises most resource bounded bounded reducibilities which can be found in the literature, including non-uniform bounded reducibilities such as P=poly T. We state conditions on bounded relations which are again satissed for most bounded reducibilities and which imply that every countable partial ordering can be embedded into every proper interval...

NP-Opt: an optimization framework for NP problems

This paper presents a new object-oriented framework for optimization based on evolutionary computation techniques to address NP-hard problems. At present, the NP-Opt is customized to deal with five classes of problems. The level of code reutilization is high and allows the adaptation to new problems very quickly, just by adding a few new classes to the framework. The structure of the classes an...

Weighted NP Optimization Problems: Logical Definability and Approximation Properties

Extending a well-known property of NP optimization problems in which the value of the optimum is guaranteed to be polynomially bounded in the length of the input, it is observed that, by attaching weights to tuples over the domain of the input, all NP optimization problems admit a logical characterization. It is shown that any NP optimization problem can be stated as a problem in which the cons...

Weighted NP Optimization Problems: Logical De nability and Approximation Properties

Optical solution for bounded NP-complete problems.

We present a new optical method for solving bounded (input-length-restricted) NP-complete combinatorial problems. We have chosen to demonstrate the method with an NP-complete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix-vector multiplication between a binary matrix, representing all feasible TSP tours, and a gray-scal...