Disjoint Segments with Maximum Density

Given a sequence A of numbers and two positive integers and k, we study the problem to find k disjoint segments of A, each has length at least , such that their sum of densities is maximized. We give the first known polynomial-time algorithm for the problem: For general k, our algorithm runs in O(n k) time. For the special case with k = 2 (respectively, k = 3), we also show how to solve the problem in O(n) (respectively, O(n + 2 )) time.

• Type: Conference
• Year: 2005
• Where: ICCS
• Authors: Yen Hung Chen, Hsueh-I Lu, Chuan Yi Tang
• Keywords: Disjoint Segments, ICCS 2005, Positive Integers, first Known Polynomial-time