Efficient Algorithms for Reconfiguration in VLSI/WSI Arrays
IEEE Transactions on Computers
Introduction to algorithms
How to play bowling in parallel on the grid
Journal of Algorithms
Pin assignment and routing on a single-layer Pin Grid Array
ASP-DAC '95 Proceedings of the 1995 Asia and South Pacific Design Automation Conference
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
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient algorithms for finding disjoint paths in grids
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On finding non-intersecting paths in grids and its application in reconfiguring VLSI/WSI arrays
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Discrete Mathematics
Reconfiguring Processor Arrays Using Multiple-Track Models: The 3Track-Spare-Approach
IEEE Transactions on Computers
Efficient Breakout Routing in Printed Circuit Boards (Extended Abstract)
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
An optimal algorithm for finding disjoint rectangles and its application to PCB routing
Proceedings of the 47th Design Automation Conference
Obstacle-avoiding free-assignment routing for flip-chip designs
Proceedings of the 49th Annual Design Automation Conference
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Given a set of sources and a set of sinks in the two dimensional grid of size n, the disjoint paths (DP) problem is to connect every source to a distinct sink by a set of edge-disjoint paths. Let v be the total number of sources and sinks. In [3], Chan and Chin showed that without loss of generality we can assume v ≤ n ≤ 4v2. They also showed how to compress the grid optimally to a dynamic network (structure of the network may change depending on the paths found currently) of size O(√nv), and solve the problem in O(√nv3/2) time using augmenting path method in maximum flow. In this paper, we improve the time complexity of solving the DP problem to O(n3/4v3/4). The factor of improvement is as large as √v when n is Θ(v), while it is at least 4√v for n is Θ(v2).