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Dominators in Linear Time
, 1997
"... A linear time algorithm is presented for finding dominators in control flow graphs. ..."
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A linear time algorithm is presented for finding dominators in control flow graphs.
A Simple and Optimal Algorithm for Finding Immediate Dominators in Reducible Graphs
, 1996
"... 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]. Dominat ..."
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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...
Polymorphic Algorithms FFTImplementations That Share
"... Abstract. We denote by a polymorphic radixn FFT an abstract algorithm scheme that is shared by all radixn FFT algorithms, similar to the way polymorphic data types share. Given such polymorphic algorithm, particular radixn algorithms can be obtained by specialization, thus need not be implemented ..."
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Abstract. We denote by a polymorphic radixn FFT an abstract algorithm scheme that is shared by all radixn FFT algorithms, similar to the way polymorphic data types share. Given such polymorphic algorithm, particular radixn algorithms can be obtained by specialization, thus need not be implemented separately. How to accomplish sharing between different radixn algorithms is not obvious: for example the four major radix2 algorithms, defining different divideandconquer 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 radixn FFT, mathematically based on the CooleyTukey 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 runtime overhead. We implemented the polymorphic radixn FFT as a C++ metaprogram.