Many algorithms spend an internal resource before returning a decision and are evaluated only by the quality of that terminal output. We formalize such procedures as terminal computation-allocation problems: costly computations produce observations, update beliefs about a latent environment, and matter only through terminal decision loss. Bellman equations characterize optimal allocation under fixed budgets, priced computation, and exact certification. We then relate value of computation (VOC) to information. Mutual information equals myopic VOC under log loss, whereas under simple regret VOC is a knowledge-gradient quantity; moreover, information gain can rank computations arbitrarily poorly, although it gives a one-sided upper bound on VOC. Bandit pulls, tree simulations, and node expansions illustrate the same model under different computation topologies. Finally, under an explicit frontier-resolution and heuristic-error model, maximizing approximate VOC recovers weighted A*, with A* and greedy best-first search as limiting cases. The theory identifies a shared decision problem without asserting that one acquisition rule is universally optimal.
Many difficult search problems cannot be solved by algorithms such as A* using only RAM. Search algorithms which use external memory such as SSDs and HDDs with much higher capacity than RAM have been proposed in previous work, but previous work has focused on delayed duplicate detection approaches, as well as complex immediate duplicate detection (IDD) methods, and relatively simple methods for IDD have not been systematically studied. In addition, the effect of OS-level mechanisms for managing and speeding up accesses to external memory, such as page caches, has not been studied. This paper addresses these gaps in the literature by evaluating and analyzing the performance of simple baseline approaches for IDD-based A*.