Improved approximation algorithms for the combination problem of parallel machine scheduling and path

Abstract

In this paper, we study a combination problem of parallel machine scheduling and the s–t path problem, which is to find a s–t path $$P_{st}$$ of the given directed graph, and to schedule the jobs corresponding to the arcs of the path $$P_{st}$$ on m parallel machines, such that the makespan is minimized. It has been proved that this problem is NP-hard and admits 2-approximation algorithm. We present a polynomial-time algorithm with approximation ratio 1.5. By modifying the dynamic programming method for the restricted shortest path problem, we also give a polynomial time approximation scheme.