Maximum-Average Segments

Years and Authors of Summarized Original Work

• 1994; Huang

Problem Definition

Given a sequence of numbers, $A=\langle a_{1},\!a_{2},\!\ldots ,a_{n}\!\rangle$, and two positive integers L, U, where 1 ≤ L ≤ U ≤ n, the maximum-density segment problem is to find a consecutive subsequence, i.e., a segment or substring, of A with length at least L and at most U such that the average value of the numbers in the subsequence is maximized.

Key Results

If there is no length constraint, then obviously the maximum-density segment is the maximum number in the sequence. Let’s first consider the problem where only the length lower bound L is imposed. By observing that the length of the shortest maximum-density segment with length at least L is at most 2L − 1, Huang [9] gave an O(nL)-time algorithm. Lin et al. [13] proposed a new technique, called the right-skew decomposition, to partition each suffix of A into right-skewsegments of strictly decreasing averages. The right-skew decomposition can be...