Issue No. 01 - January (1993 vol. 4)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.205653
<p>The problem of scheduling n independent jobs on an m-dimensional hypercube system to minimize the finish time is studied. Each job J/sub i/, where 1>or=i>or=n, is associated with a dimension d/sub i/ and a processing time t/sub i/, meaning that J/sub i/ needs a d/sub i/-dimensional subcube for t/sub i/ units of time. When job preemption is allowed, an O(n/sup 2/ log/sup 2/ n) time algorithm which can generate a minimum finish time schedule with at most min(n-2,2/sup m/-1) preemptions is obtained. When job preemption is not allowed, the problem is NP-complete. It is shown that a simple list scheduling algorithm called LDF can perform asymptotically optimally and has an absolute bound no worse than 2-1/2/sup m/. For the absolute bound, it is also shown that there is a lower bound (1+ square root 6)/2 approximately=1.7247 for a class of scheduling algorithms including LDF.</p>
Index TermsLDF algorithm; job scheduling; hypercube; job preemption; minimum finish time schedule; NP-complete; list scheduling algorithm; absolute bound; lower bound; scheduling algorithms; computational complexity; distributed algorithms; hypercube networks; scheduling
Y. Zhu and M. Ahuja, "On Job Scheduling on a Hypercube," in IEEE Transactions on Parallel & Distributed Systems, vol. 4, no. , pp. 62-69, 1993.