A Linear-Time Algorithm for Finding All Double-Vertex Dominators of a Given Vertex

TL;DR

This paper introduces a linear-time algorithm and data structure for efficiently identifying all double-vertex dominators of a given vertex in a graph, aiding in analyzing reconverging paths in circuit graphs.

Contribution

It presents the first linear-time algorithm for finding all double-vertex dominators and a linear-space data structure for their representation.

Findings

Efficient linear-time algorithm for double-vertex dominator detection

Linear-space data structure for representing all double-vertex dominators

Facilitates analysis of reconverging paths in large graphs

Abstract

Dominators provide a general mechanism for identifying reconverging paths in graphs. This is useful for a number of applications in Computer-Aided Design (CAD) including signal probability computation in biased random simulation, switching activity estimation in power and noise analysis, and cut points identification in equivalence checking. However, traditional single-vertex dominators are too rare in circuit graphs. In order to handle reconverging paths more efficiently, we consider the case of double-vertex dominators which occur more frequently. First, we derive a number of specific properties of double-vertex dominators. Then, we describe a data structure for representing all double-vertex dominators of a given vertex in linear space. Finally, we present an algorithm for finding all double-vertex dominators of a given vertex in linear time. Our results provide an efficient systematic way of partitioning large graphs along the reconverging points of the signal flow.