This book is about problem solving. Specifically, it is about heuristic state-space search under branch-and-bound framework for solving comΒ binatorial optimization problems. The two central themes of this book are the average-case complexity of heuristic state-space search algorithms based on branch-and-bound, and their applications to developing new problem-solving methods and algorithms. Heuristic state-space search is one of the fundamental problem-solving techniques in Computer Science and Operations Research, and usually constitutes an important component of most intelligent problem-solving systems. The search algorithms considered in this book can be classified into the category of branch-and-bound. Branch-and-bound is a general problem-solving paradigm, and is one of the best techniques for optimally solving computation-intensive problems, such as scheduling and planning. The main search algorithms considered include best-first search, depthΒ first branch-and-bound, iterative deepening, recursive best-first search, and space-bounded best-first search. Best-first search and depth-first branch-and-bound are very well known and have been used extensively in Computer Science and Operations Research. One important feature of depth-first branch-and-bound is that it only requires space this is linear in the maximal search depth, making it very often a favorable search algoΒ rithm over best-first search in practice. Iterative deepening and recursive best-first search are the other two linear-space search algorithms. Iterative deepening is an important algorithm in Artificial Intelligence, and plays an irreplaceable role in building a real-time game-playing program.