No abstract

For P-complete problems such as traveling salesperson, cycle covers, 0-1 integer programming, multicommodity network flows, quadratic assignment, etc., it is shown that the approximation problem is also P-complete. In contrast with these results, a linear time approximation algorithm for the clustering problem is presented.

A linear time algorithm to obtain a minimum finish time schedule for the two-processor open shop together with a polynomial time algorithm to obtain a minimum finish time preemptive schedule for open shops with more than two processors are obtained. It is also shown that the problem of obtaining minimum finish time nonpreemptive schedules when the open shop has more than two processors is NP-complete.

We show that finding minimum finish time preemptive and non-preemptive schedules for flow shops and job shops is NP-complete. Bounds on the performance of various heuristics to generate reasonably good schedules are also obtained.

AaSTRACT An O(n) t~me algorithm is presented to obtain an opt,mal fimsh time preemptive schedule for n independent tasks on m uniform processors This algorithm assumes that the tasks are lnmally ordered by task length and that the umform processors are ordered by processor speed KEY WORDS AND PHRASES. uniform processors, preemptive schedules, optimal fimsh time schedules, mdependent tasks CR CATEGORIES" 4 32, 5 39