A linear time algorithm is presented for finding dominators in control flow graphs.

We present two simple algorithm for finding immediate dominator in reducible graphs with n nodes and m edges: A O(n + m) RAM algorithm and a O(n +m log log n) pointer machine algorithm. 1 Introduction Algorithms for finding dominator trees for control flow graphs are described in [5, 7, 8]. Dominator trees are used in control flow analysis [1, 4]. In [5] a linear time algorithm is given. This algorithm is complicated and to our knowledge no experimental results using this algorithm have been published. This is the motivation for presenting two simpler algorithms, one of which runs on a pointer machine [10]. The algorithms presented in this paper have previously been described by the authors of this paper and also independently and simultaneously in [9]. But at that time the important results from [2, 3], were not applied, so the contribution of this paper is only a compilation. 2 Notation A control flow graph CFG(V;E; s) is a directed graph with a start node s, from which all nodes i...

Abstract. We denote by a polymorphic radix-n FFT an abstract algorithm scheme that is shared by all radix-n FFT algorithms, similar to the way polymorphic data types share. Given such polymorphic algorithm, particular radix-n algorithms can be obtained by specialization, thus need not be implemented separately. How to accomplish sharing between different radix-n algorithms is not obvious: for example the four major radix-2 algorithms, defining different divide-and-conquer schemes and working for different input formats, have little in common at the implementation level. At a higher level of abstraction, however, it is possible to provide a unifying framework. In this paper we introduce a polymorphic radix-n FFT, mathematically based on the Cooley-Tukey mapping, and show how to effectively realize this mapping using techniques from generic programming. Since specializations can take place entirely at compile time, their generalization does not incur any run-time overhead. We implemented the polymorphic radix-n FFT as a C++ meta-program.