Graph search is used in many areas of computer science. It is well-known that the scalability of graph-search algorithms such as A* is limited by their memory requirements. In this dissertation, I describe three complementary strategies for reducing the memory requirements of graph-search algorithms, especially for multiple sequence alignment (a central problem in computational molecular biology). These search strategies dramatically increase the range and difficulty of multiple sequence alignment problems that can be solved. The first strategy uses a divide-and-conquer method of solution reconstruction, and one of my contributions is to show that when divide-and-conquer solution reconstruction is used, a layer-by-layer strategy for multiple sequence alignment is more memory-efficient than a bestirst strategy. The second strategy is a new approach to duplicate detection in external-memory graph search that involves partitioning the search graph based on an abstraction of the state space. For graphs with sufficient local structure, it allows graph-search algorithms to use external memory, such as disk storage, almost as efficiently as internal memory. The third strategy is a technique for reducing the memory requirements of sub-alignment search heuristics that are stored in lookup tables. It uses the start and goal states of a problem instance to restrict the region of the state space for which a table-based heuristic is needed, making it possible to store more accurate heuristic estimates in the same amount of memory. These three strategies dramatically improve the scalability of graph search not only for multiple sequence alignment, but for many other graph-search problems, and generalizations of these search strategies for other graph-search problems are discussed throughout the dissertation.