On a Geometric Approach to the Segment Sum Problem and Its Generalization

Given a sequence of n real numbers a1, a2, a3, . . . , an, the maximum segment sum problem is that of determining indices i and j (1 ≤ i ≤ j ≤ n) such that the sum s(i, j) = ai + ai+1 + . . . + aj is a maximum. Monotone matrices were shown to be remarkably effective in solving several geometric optimization problems. The surprise is that it can also be applied to the above problem as we show here. Recently, there was a breakthrough in obtaining an O(n log n) algorithm for the kth smallest segment sum problem by exploiting a connection of this problem to the well-known slope selection problem. In this paper we show that this problem can also be solved within the same time bounds in the simpler framework of expander graphs.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Asish Mukhopadhyay, Eugene Greene
• Keywords: CCCG 2007, Computational Geometry, Maximum Segment Sum, Segment Sum Problem, Smallest Segment Sum