Introduction to algorithms
Fast evaluation of sequence pair in block placement by longest common subsequence computation
DATE '00 Proceedings of the conference on Design, automation and test in Europe
A fast algorithm for computing longest common subsequences
Communications of the ACM
FAST-SP: a fast algorithm for block placement based on sequence pair
Proceedings of the 2001 Asia and South Pacific Design Automation Conference
Simultaneous escape routing and layer assignment for dense PCBs
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
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
Theories and algorithms on single-detour routing for untangling twisted bus
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Optimal layer assignment for escape routing of buses
Proceedings of the 2009 International Conference on Computer-Aided Design
An optimal algorithm for finding disjoint rectangles and its application to PCB routing
Proceedings of the 47th Design Automation Conference
Optimal simultaneous pin assignment and escape routing for dense PCBs
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
A provably good approximation algorithm for rectangle escape problem with application to PCB routing
Proceedings of the 16th Asia and South Pacific Design Automation Conference
New optimal layer assignment for bus-oriented escape routing
Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI
An optimal algorithm for layer assignment of bus escape routing on PCBs
Proceedings of the 48th Design Automation Conference
Recent research development in PCB layout
Proceedings of the International Conference on Computer-Aided Design
Density-reduction-oriented layer assignment for rectangle escape routing
Proceedings of the great lakes symposium on VLSI
New optimal layer assignment for bus-oriented escape routing
Integration, the VLSI Journal
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The PCB routing problem has become so difficult that no commercial CAD software can provide an automatic solution for high-end boards. Existing algorithms for escape routing, an important step in PCB routing, are net-centric. Directly applying these algorithms will result in mixing nets of different buses together. But in practice, it is preferred to bundle together nets in a bus. Thus the bus-centric escape routing problem can be naturally divided into two subproblems: (1) finding a subset of buses that can be routed on the same layer without net mixings and crossings, which we refer to as the bus sequencing problem, and (2) finding the escape routing solutions for each chosen bus, which can be solved by a net-centric escape router. In this paper, we solve the bus sequencing problem. We introduce a new optimization problem called the Longest Common Interval Sequence (LCIS) problem and model the bus sequencing problem as an LCIS problem. By using dynamic programming and balanced search tree data structure, we present an LCIS algorithm which can find an optimal solution in O(n log n) time. We also show that O(n log n) is a lower-bound for this problem and thus the time complexity of our algorithm is also the best possible.