The principle of Selecten Jumping Searching andC,C ^′₀ ,C ^* algorithms

Abstract

A new searching approach, Selecten Jumping Searching (SJS), in which the length of every seaching step from a node to another node along a path is much longer than one, has been proposed this paper. In addition to all the problems which can be solved by GPS or MPS, SJS can also solve other problems such as theN Queens problems, theN Puzzle problems, etc., which GPS and MPS fail whenN is large and whose computational complexity are exponential by the general searching approach or MPS. The searching algorithms of SJS, algorithmsC,C ₀ (orC ^′₀ ) andC ^* whose computational complexity is only polynomial and linear respectively have been proposed also in this paper. Finally, the experimental results of the Five Hundred Queens problem, more than two Thousand Queens problem and theN Puzzle problem (whereN is more than one thousand) are given. In order to get the first some solutions of the Fifty Queens problem and to build the 35²−1 Puzzle problem’s Macro Table of MPS, both of them would take 10²⁵ years even using a 10¹⁵ ops supercomputer by the general searching approach. But using proposed approach and algorithms (whose computational complexity isO(N) andO(N ^3/2) respectively), 4000 solutions of the Five Hundred Queens problem have been got when program runs about 227 minutes on HP 9000/835 and the average solution time to solve the 35²−1 Puzzle problem with arbitrary problem state is less than one minute on HP 9000/300. SJS is a searching approach as a result mapped from Macro Transformation approach.