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Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works only consider how to find one longest common subsequence. In this paper, we consider how to determine the uniqueness of the longest common subsequence. If there are multiple longest common subsequences, we also determine which number appears in all/some/none of the longest common subsequences. We focus on four scenarios: (1) linear sequences without duplicated numbers; (2) circular sequences without duplicated numbers; (3) linear sequences with duplicated numbers; (4) circular sequences with duplicated numbers. We develop corresponding algorithms and apply them to gene sequencing data. [ABSTRACT FROM AUTHOR]

Most of the FPGA's area and delay are due to routing. Considering routability at earlier steps of the CAD flow would both yield better quality and faster design process. In this paper, we discuss the metrics that affect routability in packing logic into clusters. We are presenting a routability-driven clustering method for cluster-based FPGAs. Our method packs LUTs into logic clusters while incorporating routability metrics into a cost function. Based on our routability model, the routability in timing-driven packing algorithm is analyzed. We integrate our routability model into a timing-driven packing algorithm. Our method yields up to 50% improvement in terms of the minimum number of routing tracks compared to VPack (16.5% on average). The average routing area improvement is 27% over VPack and 12% over t-VPack. [ABSTRACT FROM AUTHOR]