Algorithm Design and Analysis
An algorithm is a formalization of constrained choice over time. It is a rule-governed process that navigates a space of possibilities, using limited information and resources, to produce outcomes that optimize, approximate, or satisfy some objective.
Different problems admit different representations. The representation we choose determines the structure of the solution space and therefore determines whether we can traverse it efficiently, exhaustively, approximately, or not at all.
Some problems are tractable: they permit finite, bounded procedures that converge to an exact solution.
Others resist finitude either due to combinatorial explosion, incomplete information, or undecidability. In such cases, we relax optimality. We search for approximations, heuristics, or satisficing solutions that respect constraints even if they do not achieve global optimality.
Algorithms, in this sense, are everywhere.
From early childhood, we are taught primitive routines; counting, comparison, imitation, language, moral heuristics. As we grow, experience acts as data. We refine weights, compose routines, prune ineffective strategies, and build higher-order abstractions.
Over time, we do not merely execute algorithms; we construct them.
The following sections document the tools, abstractions, and reasoning patterns that have helped me navigate complex problems. They are written from first principles so they remain composable, extensible, and adaptable.