Scheduling independent tasks on partitionable hypercube multiprocessors

A partitionable hypercube allows simultaneous execution of multiple tasks, where each task can be executed on a choice of subcubes. This paper considers the problem of static nonpreemptive scheduling of w independent tasks on a n processor partitionable hypercube system to minimize the overall finishing time of the w tasks. Each task can be executed on subcubes of different sizes, with smaller execution times on larger subcubes. A schedule determines the size of the subcube to be assigned to each task and schedules these tasks on the processors in the hypercube system. The problem of finding the optimal schedule, with minimum finishing time, is known to be NP-hard. This paper presents a fast polynomial time approximation algorithm for the problem, and derives a tight worst-case performance bound of 2 for the algorithm