Path complexity of maximum segment sum problem

Abstract

Various software complexity metrics have been proposed in literature. A program complexity measure called path complexity is proposed in [1]. Path complexity P(A,n) of an algorithm A is defined to be the number of program execution paths of A over all inputs of size n. It defines a partition of input space of program A into equivalence classes on the basis of different program execution paths. All the inputs belonging to an equivalence class are equivalent to each other in a sense that they follow same execution path. We present path complexity analysis of four different algorithms for one-dimensional maximum segment sum problem which shows that algorithms with different computational complexity may be equivalent to each other in their path complexity. We also present lower bounds on one dimensional as well as two dimensional maximum segment-sum problems. A different perspective and several observations on one dimensional problem are given