Analyzing the asymptotic complexity of problems already known to be polynomial time solvable. Often, conditional lower bounds are used to show that a specific algorithm is asymptotically optimal.
Fine-Grained Analysis
This term have been used frequently in recent papers, to indicate to analyses of algorithms/reduction with high attention to details of the given method. In contrast to coarse-grained analysis, fine-grained analysis contains deeper inspecting of single steps. It sets finer bounds on the running times and the constructed structures to achieve finer total running time. It is used mostly in conditional lower-bound, string matching algorithms and distributed models of computing.
