The physical design placement problem is one of the hardest and most important problems in micro chips production. The placement defines how to place the electrical components on the chip. We consider the problem as a combinatorial optimization problem, whose instance is defined by a set of $2$-dimensional rectangles, with various sizes and wire connectivity requirements. We focus on minimizing the placement area and the total wire length.
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An instance of a weighted Stackelberg load balancing game is given by a set of identical machines, a set of variable-length jobs and a parameter 0 ≤ α ≤ 1. A centralized authority, denoted the leader, selects a subset of the jobs whose total length is at most an α-fraction of the total length and determines their assignment on the machines. After the controlled jobs are assigned, the remaining jobs join the schedule. They act selfishly, each determining its own assignment. Our work combines theoretical and experimental results for this setting. We suggest various heuristics for the leader and analyze their performance.
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