An efficient algorithm for finding double-vertex dominators in circuit graphs

Graph dominators provide a general mechanism for identifying re-converging paths in circuits. This is useful in a number of CAD applications, including computation of signal probabilities for test generation, switching activities for power and noise analysis, statistical timing analysis, cut point selection in equivalence checking, etc. Single-vertex dominators are too rare in circuit graphs to handle re-converging paths in a practical way. The paper addresses the problem of finding double-vertex dominators, which occur more frequently. First, we introduce a data structure, called dominator chain, which allows the representation of all possible O(n²) double-vertex dominators of a given vertex in O(n) space, where n is the number of vertices of the circuit graph. Dominator chains can be efficiently manipulated, e.g., it takes constant time to look-up whether a given pair of vertices is a double-vertex dominator. Second, we present an efficient algorithm for finding double-vertex dominators. The experimental results show that the presented algorithm is an order of magnitude faster than existing algorithms for finding double-vertex dominators. Thus, it is suitable for running in an incremental manner during logic synthesis.