Abstract
This paper studies scheduling game with machine modification in the random setting. A set of jobs is to be processed on a set of identical machines. An initial schedule before the modification of machines is given as a prior. Then some machines are removed and some new machines are added. Each job has the right either to stay on its original machine if the machine is not removed, or to move to another machine. If one job changes its machine, it will be behind of all the former jobs scheduled on the target machine. For two jobs moving to the same machine or two jobs staying on the same machine, each one of them has the same probability to be ahead of the other one. The individual cost of each job is its completion time, and the social cost is the makespan. We present properties of the Nash Equilibrium and establish the Price of Anarchy of the game. The bounds are tight for each combination of the number of final machines, the number of added machines and the number of removed machines.
C. He—Supported by the National Natural Science Foundation of China (11801505).
Z. Tan—Supported by the National Natural Science Foundation of China (11671356).
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He, C., Tan, Z. (2019). Scheduling Game with Machine Modification in the Random Setting. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_21
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DOI: https://doi.org/10.1007/978-3-030-36412-0_21
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