With more and more biological sequences available, sequence analyses have become very important in bioinformatics and computational biology. In this book, we present the results of our research on genome sequence alignment, RNA folding with simple pseudoknots, and single nucleotide polymorphism (SNP) association pattern discovery with spatial constraints. In genome sequence alignment, we use the divide and conquer approach to reduce the computational complexity of multiple whole genome sequence alignment. Furthermore, we introduced the concept of solution space of genome sequence alignment to solve the problem that the current genome sequence alignment algorithms do not consider spatial constraints. The solution space is modeled as a multi-bipartite digraph. We provide efficient graph decomposition and traversal algorithms for processing the graph to output solutions as alignments of functionally equivalent clusters.