Non-Deterministic and Polynomial Time Problem Simulator

A Polynomial-Time Deterministic Approach to the Traveling Salesperson Problem

We propose a new polynomial-time deterministic algorithm that produces an approximated solution for the traveling salesperson problem. The proposed algorithm ranks cities based on their priorities calculated using a power function of means and standard deviations of their distances from other cities and then connects the cities to their neighbors in the order of their priorities. When connectin...

NON-POLYNOMIAL QUARTIC SPLINE SOLUTION OF BOUNDARY-VALUE PROBLEM

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

An Explicit Separation of Relativised Random Polynomial Time and Relativised Deterministic Polynomial Time

Using SAT and Logic Programming to Design Polynomial-Time Algorithms for Planning in Non-Deterministic Domains

We show that a Horn SAT and logic programming approach to obtain polynomial time algorithms for problem solving can be fruitfully applied to finding plans for various kinds of goals in a non-deterministic domain. We particularly focus on finding weak, strong, and strong cyclic plans for planning problems, as they are the most studied ones in the literature. We describe new algorithms for these ...

Analysis of the Deterministic Polynomial Time Solvability of the 0-1-Knapsack Problem

Previously the author has demonstrated that a representative polynomial search partition is required to solve a NP-complete problem in deterministic polynomial time. It has also been demonstrated that finding such a partition can only be done in deterministic polynomial time if the form of the problem provides a simple method for producing the partition. It is the purpose of this article to dem...