Introduction to algorithms
Placement and routing tools for the Triptych FPGA
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Single-layer fanout routing and routability analysis for Ball Grid Arrays
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Efficient breakout routing in printed circuit boards
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Escaping a grid by edge-disjoint paths
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
VPR: A new packing, placement and routing tool for FPGA research
FPL '97 Proceedings of the 7th International Workshop on Field-Programmable Logic and Applications
Efficient escape routing for hexagonal array of high density I/Os
Proceedings of the 43rd annual Design Automation Conference
MCM technology and design for the S/390 G5 system
IBM Journal of Research and Development
Algorithms for simultaneous escape routing and Layer assignment of dense PCBs
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Simultaneous Escape-Routing Algorithms for Via Minimization of High-Speed Boards
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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As the circuit densities and transistor counts are increasing, the package routing problem is becoming more and more challenging. In this article, we study an important routing problem encountered in typical high-end MCM designs: routing within dense pin clusters. Pin clusters are often formed by pins that belong to the same functional unit or the same data bus, and can become bottlenecks in terms of overall routability. Typically, these clusters have irregular shapes, which can be approximated with rectilinear convex boundaries. Since such boundaries have often irregular shapes, a traditional escape routing algorithm may give unroutable solutions. In this article, we study how the positions of escape terminals on a convex boundary affect the overall routability. For this purpose, we propose a set of necessary and sufficient conditions to model routability outside a rectilinear convex boundary. Given an escape routing solution, we propose an optimal algorithm to select the maximal subset of nets that are routable outside the boundary. After that, we focus on an integrated approach to consider routability constraints (outside the boundary) during the actual escape routing algorithm. Here, we propose an optimal algorithm to find the best escape routing solution that satisfies all routability constraints. Our experiments demonstrate that we can reduce the number of layers by 17% on the average, by using this integrated methodology.