Improved approximation algorithms for scheduling with release dates

Conference · Sun Jun 01 04:00:00 EDT 1997

OSTI ID:471717

Goemans, M X ^[1]

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1. MIT, Cambridge, MA (United States)

We consider the scheduling problem of minimizing a weighted sum of completion times under release dates. We present a simple randomized 2-approximation algorithm for the problem running in O(n log n) time. The algorithm applies to both the off-line and on-line settings with no difference in performance guarantees. In the off-line setting, the algorithm can be derandomized in two different ways, leading either to a deterministic 2-approximation algorithm running in O(n{sup 2}) time, or to a 2+1/{kappa}-approximation algorithm IC running in O(n log n + kn) time. In the on-line setting, a specific random choice gives a deterministic 1 + {radical}2-competitive algorithm. These bounds improve upon a bound of 2.45 in the off-line setting or in the randomized on-line setting, and upon a bound of 3 + {epsilon} in the deterministic on-line setting, it is based on comparing the weight of the schedule produced to the value of a linear programming (LP) relaxation. However, the algorithm and analysis differ from the approach developed in several respects. First, we simultaneously consider two equivalent LP relaxations for the problem: one involving completion time variables, the other preemptive time-indexed variables. The design of the algorithm is essentially based on the time-indexed relaxation; its analysis is based on the completion time relaxation. Moreover, we exploit properties of the optimum solutions to these LP relaxations, and not just of any feasible solution. Another important difference is that we do not relate directly the completion time of job j with its fractional completion time, but only in an amortized sense. Finally, we use randomization to avoid adversarial situations; this last step can also be seen as constructing n different schedules and keeping the best of them.

• OSTI ID: 471717
• Report Number(s): CONF-970142--; CNN: Contract 9302476-CCR; Contract 9623859; Contract N00014-95-1-1246
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
LINEAR PROGRAMMING
SCHEDULES
TASK SCHEDULING
TIME DEPENDENCE