THE MODELING OF RDB AND THE IMPROVEMENT OF MILLER'S CONCLUSION

Abstract

This paper is dealt with the RDB(Restricted Difference Basis) problem .Let Kn be a complete graph of order n and k(n) be the number of all the edges of Kn .Miller proved that for n large enough the number f(n) of edges that can be labeled continuously in Kn is about one third of k(n) .In this paper we establish a 'x link' marks distribution model of RDB ruler .By using the model the following results are proved:

f(n)>=k(n+1)/2 for n>=3;
f(n)>=k(n+2)/2 for n>=9;
f(n)>=k(n+3)/2 for n>=33;
f(n)>=k(n+4)/2 for n>=409.
Thus the Miller's conclusion is improved.