Finding dominators via disjoint set union

Finding dominators via disjoint set union

The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-lineartime algorithms exist, they use sophisticated data structures. We develop an algorithm for finding dominators that uses only a “static tree” disjoint set data structure in addition to simple lists and maps. The algorithm runs in n...

Disjoint Set Union with Randomized Linking

A classic result in the analysis of data structures is that path compression with linking by rank solves the disjoint set union problem in almost-constant amortized time per operation. Recent experiments suggest that in practice, a näıve linking method works just as well if not better than linking by rank, in spite of being theoretically inferior. How can this be? We prove that randomized linki...

Finding Dominators in Practice

The computation of dominators in a flowgraph has applications in several areas, including program optimization, circuit testing, and theoretical biology. Lengauer and Tarjan [30] proposed two versions of a fast algorithm for finding dominators and compared them experimentally with an iterative bit-vector algorithm. They concluded that both versions of their algorithm were much faster even on gr...

Finding Dominators Revisited

The problem of finding dominators in a flowgraph arises in many kinds of global code optimization and other settings. In 1979 Lengauer and Tarjan gave an almost-linear-time algorithm to find dominators. In 1985 Harel claimed a lineartime algorithm, but this algorithm was incomplete; Alstrup et al. [1999] gave a complete and “simpler” linear-time algorithm on a random-access machine. In 1998, Bu...

Finding Dominators in Directed Graphs