An Optimal Algorithm for the Maximum-Density Segment Problem

We address a fundamental problem arising from analysis of biomolecular sequences. The input consists of two numbers wmin and wmax and a sequence S of n number pairs (ai, wi) with wi > 0. Let segment S(i, j) of S be the consecutive subsequence of S between indices i and j. The density of S(i, j) is d(i, j) = (ai +ai+1 +· · ·+aj)/(wi +wi+1 +· · ·+wj). The maximum-density segment problem is to find a maximum-density segment over all segments S(i, j) with wmin ≤ wi + wi+1 + · · · + wj ≤ wmax. The best previously known algorithm for the problem, due to Goldwasser, Kao, and Lu, runs in O(n log(wmax −wmin +1)) time. In the present paper, we solve the problem in O(n) time. Our approach bypasses the complicated right-skew decomposition, introduced by Lin, Jiang, and Chao. As a result, our algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genomescale sequences. Moreover, for a type of input sequences...

• Type: Conference
• Year: 2003
• Where: ESA
• Authors: Kai-min Chung, Hsueh-I Lu
• Keywords: ESA 2003, Fundamental Problem, Maximum-density Segment, Maximum-density Segment Problem