By Trinder P.
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Extra info for A functional database
Smith-rule, then the coordination ratio is at most 4, moreover this is best possible among nonpreemptive policies. Then we establish our main result. We design a preemptive policy, externality, that extends Smith-rule by adding extra delays on the jobs accounting for the negative externality they impose on other players. 618, and complement this result by proving that this ratio is best possible even if we allow for randomization or full information. Finally, we establish that this externality policy induces a potential game and that an ε-equilibrium can be found in polynomial time.
Throughout the paper, x∗ denotes the optimal assignment (thus x∗ is a pure strategy), and we deﬁne Xi∗ as the set of jobs assigned to machine i under the optimal assignment. Given the assignment of jobs to machines, it is well-known that Smith Rule minimizes the total cost of jobs. Therefore C ×Ö (x∗ ) is the optimal cost. Optimal Coordination Mechanisms for Multi-job Scheduling Games 2 19 Nonpreemptive Mechanisms We now study nonpreemptive mechanisms (jobs have IDs, needed to break ties between identically looking jobs) and prove that ×Ö has a coordination ratio of 4 for mixed WE.
Therefore C ×Ö (x∗ ) is the optimal cost. Optimal Coordination Mechanisms for Multi-job Scheduling Games 2 19 Nonpreemptive Mechanisms We now study nonpreemptive mechanisms (jobs have IDs, needed to break ties between identically looking jobs) and prove that ×Ö has a coordination ratio of 4 for mixed WE. We work with mixed strategies since ×Ö does not guarantee that existence of pure WE. As mentioned earlier, our result is best possible among nonpreemptive mechanisms . Recall that under ×Ö, each machine i schedules nonpreemptively its assigned jobs j in nondecreasing order of ρij = pij /wj , and ties are broken using the IDs.
A functional database by Trinder P.