Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
First- and second-level packaging of the z990 processor cage
IBM Journal of Research and Development
An escape routing framework for dense boards with high-speed design constraints
ICCAD '05 Proceedings of the 2005 IEEE/ACM International conference on Computer-aided design
Routing algorithms for high-performance vlsi packaging
Routing algorithms for high-performance vlsi packaging
Optimal bus sequencing for escape routing in dense PCBs
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Automatic bus planner for dense PCBs
Proceedings of the 46th Annual Design Automation Conference
First- and second-level packaging for the IBM eServer z900
IBM Journal of Research and Development
An optimal algorithm for finding disjoint rectangles and its application to PCB routing
Proceedings of the 47th Design Automation Conference
Density-reduction-oriented layer assignment for rectangle escape routing
Proceedings of the great lakes symposium on VLSI
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In this paper, we introduce and study the Rectangle Escape Problem (REP), which is motivated by 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 Program (ILP). A provably good approximation algorithm for the REP is developed by applying Linear Programming (LP) relaxation and a special rounding technique to the ILP. This approximation algorithm is also shown to work for a more general version of REP with weights (weighted REP). In addition, an iterative refinement procedure is proposed as a postprocessing step to further improve the results. Our approach is tested on a set of industrial PCB bus escape routing problems. Experimental results show that the optimal solution can be obtained within 3 seconds for each of the test cases.