NP-Completeness and an Approximation Algorithm for Rectangle Escape Problem With Application to PCB Routing

@article{Ma2012NPCompletenessAA,
  title={NP-Completeness and an Approximation Algorithm for Rectangle Escape Problem With Application to PCB Routing},
  author={Qiang Ma and Martin D. F. Wong},
  journal={IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems},
  year={2012},
  volume={31},
  pages={1356-1365}
}
In this paper, we introduce and study the rectangle escape problem (REP), which is motivated by printed circuit board (PCB) bus escape routing. Given a rectangular region R and a set S of rectangles within R, the REP is to choose a direction for each rectangle to escape to the boundary of R, such that the resultant maximum density over R is minimized. We prove that the REP is NP-complete, and show that it can be formulated as an integer linear programming (ILP). A provably good approximation… CONTINUE READING

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