Study In The Problems And Algorithms Of Multi-magic Square

Magic square originated thousands of years ago in China, from the date of magic square appears, have been active in people's daily life, with a trace of mystery. In 1890, a French mathematician published the first 8 order bi-magic square, make this magic square world which was originally mysterious become more complicated and confusing. Since then, people do not be content to constructing a magic square which is common as before, but pursuit to construct a multi-magic square which meet the conditions of the multi-magic sums. However how to construct multi-magic square is a very difficult problem, especially these low-order multi-magic squares, which are very difficult.A pleasant surprise is that the rapid development of computer science has brought new vitality for the study of magic square, high-speed operation of a computer system that can replace the human brain to complete the duplication of tedious tasks and construct a complex multi-magic square. However, multi-magic square is a typical NP problem, time complexity that computer search a magic square are more than people think. To construct a multi-magic square in a short period of time, we must design good algorithm. We can use the idea of backtracking search to design multi-magic square algorithm, and for some specific examples we make specific adjustments, so we can more quickly in time to construct a multi-magic square.This paper describes the characteristics of multi-magic squares, and general idea to use computer to solve multi-magic square problem. Through study and analysis, found that most of the odd-order multi-magic squares have numbers which are on the center of symmetry; if you use this feature to design some algorithm that construct odd-order multi-magic square, you can find a multi-magic square within a very short time. Finally we design a representative 13th order bi-magic square algorithm, and described a thinking framework which is used by computer to search a magic square solution space. This algorithm has a certain reference value for the study of other types of multi-magic squares and other NP problems.