Online uniformity of integer points on a line
This Letter presents algorithms for computing a uniform sequence of it integer points in a given interval vertical bar 0. m vertical bar where m and n are integers such that m > n > 0. The uniformity of a point set is measured by the ratio of the minimum gap over the maximum gap. We prove that we can insert it integral points one by one into the interval vertical bar 0. m vertical bar while keeping the uniformity of the point set at least 1/2. If we require uniformity strictly greater than 1/2, such a sequence does not always exist, but we can prove a tight tipper bound oil the length of the sequence for given values of n and m. (C) 2008 Elsevier B.V. All rights reserved.
uniformity algorithms discrepancy computational geometry