We consider the classical online scheduling problem over single and parallel machines with the objective of minimizing total weighted flow time. We employ an intuitive and systematic analysis method and show that the weighted shortest processing time (WSPT) is an optimal online algorithm with the competitive ratio of +1 for the case of single machine, and it is ( +(3/2)−(1/2 ))-competitive for the case of parallel machines ( > 1), where P is the ratio of the longest to the shortest processing time.
Moreover, Weighted Shortest Processing Time (WSPT) is a O(Δ + 3 2 − 1 2m )-competitive algorithm REF for the more general problem where each task has a weight and the objective is to minimize the total weighted flow-time.
WSPT's Competitive Performance for Minimizing the Total Weighted Flow Time: From Single to Parallel Machines
Mathematical Problems in Engineering
Computer Science