Efficient routability check algorithms for segmented channel routing

Abstract

The segmented channel-routing problem arises in the context of row-based field programmable gate arrays (FPGAs). Since the K -segment channel-routing problem is NP-complete for K ≥ 2, an efficient algorithm using the weighted bipartite-matching approach is developed for this problem. Connections that;form a maximum clique are chosen first to be routed to the segmented channel. Then, another maximum clique of the remained connections is routed until all connections have been processed. In addition, a powerful “unroutability check” algorithm is uniquely proposed to tell whether the horizontal switches in an interval of the segmented channel are sufficient for routing or not. Hence, we can precisely discriminate the routable and the unroutable ones from all the test cases. As shown in the experiments, average discrimination ratios of 98.8% and 99.4% are obtained for the 2-segmentation and 3-segmentation models, respectively. Moreover, when applying our routing algorithm to the analyzed nonunroutable cases, a routing failure ratio of 1.5% is reported for the 2-segmentation model, compared to Zhu and Wong's 5.9%; also, a routing failure ratio of 0.8% (less than their 4.7%) is obtained for the 3-segmentation model. In total, the routing failure ratio of our routing algorithm is less than 21% of Zhu and Wong's.