The problem of finding the dominators in a control-flow graph has a long history in the literature. The original algorithms su#ered from a large asymptotic complexity but were easy to understand. Subsequent work improved the time bound, but generally sacrificed both simplicity and ease of implementation. This paper returns to a simple formulation of dominance as a global data-flow problem. Some insights into the natureofdominance lead to an implementation of an O(N )algorithm that runs faster, in practice, than the classic Lengauer-Tarjan algorithm, which has a timebound of O(E log(N)). We compare the algorithm to Lengauer-Tarjan because it is the best known and most widely used of the fast algorithms for dominance. Working from the same implementationinsights,wealso rederive (from earlier work on control dependence by Ferrante, et al.)amethodforcalculating dominance frontiers that we show is faster than the original algorithm by Cytron, et al. The aim of this paper is not to present a new algorithm, but, rather, to make an argument based on empirical evidence that algorithms with discouraging asymptotic complexities can be faster in practice than those more commonly employed. We show that, in some cases, careful engineering of simple algorithms can overcome theoretical advantages, even when problems grow beyond realistic sizes. Further, we argue that the algorithms presented herein are intuitive and easily implemented, making them excellent teaching tools.

We introduce the tree cross-product problem, which abstracts a data structure common to applications in graph visualization, string matching, and software analysis. We design solutions with a variety of tradeoffs, yielding improvements and new results for these applications.

This paper explores the concept of loops and loop nesting forests of control-flow graphs, using the problem of constructing the dominator tree of a graph and the problem of computing the iterated dominance frontier of a set of vertices in a graph as guiding applications. The contributions of this paper include: (1) An axiomatic characterization, as well as a constructive characterization, of a family of loop nesting forests that includes various specific loop nesting forests that have been previously defined. (2) The definition of a new loop nesting forest, as well as an e#cient, almost linear time, algorithm for constructing this forest. (3) An illustration of how loop nesting forests can be used to transform arbitrary (potentially irreducible) problem instances into equivalent acylic graph problem instances in the case of the two problems of (a) constructing the dominator tree of a graph, and (b) computing the iterated dominance frontier of a set of vertices in a graph, leading to new, almost linear time, algorithms for these problems

This paper introduces a modification of Agrawal's algorithm for slicing unstructured programs, which overcomes these difficulties. The new algorithm produces thinner slices than any previously published algorithm while respecting both the semantic and syntactic constraints of slicing. c fl1998 by John Wiley & Sons, Ltd.

The purpose of this paper is to introduce frameworks based on data-flow equations which provide for estimating the worst-case execution time (WCET) of (real-time) programs. These frameworks allow several different WCET analysis techniques, which range from nave approaches to exact analysis, provided exact knowledge on the program behaviour is available. However, data-flow frameworks can also be used for symbolic analysis based on information derived automatically from the source code of the program. As a byproduct we show that slightly modified elimination methods can be employed for solving WCET data-flow equations, while iteration algorithms cannot be used for this purpose.

This paper proposes a novel algorithm that, given a data-flow graph and an input/output constraint, enumerates all convex subgraphs under the given constraint in polynomial time with respect to the size of the graph. These subgraphs have been shown to represent efficient Instruction Set Extensions for customizable processors. The search space for this problem is inherently polynomial but, to our knowledge, this is the first paper to prove this and to present a practical algorithm for this problem with polynomial complexity. Our algorithm is based on properties of convex subgraphs that link them to the concept of multiple-vertex dominators. We discuss several pruning techniques that, without sacrificing the optimality of the algorithm, make it practical for data-flow graphs of a thousands nodes or more. 1.

Identification of behavioural contradictions is an important aspect of software engineering, in particular for checking the consistency between a business process model used as system specification and a corresponding workflow model used as implementation. In this paper, we propose causal behavioural profiles as the basis for a consistency notion, which capture essential behavioural information, such as order, exclusiveness, and causality between pairs of activities. Existing notions of behavioural equivalence, such as bisimulation and trace equivalence, might also be applied as consistency notions. Still, they are exponential in computation. Our novel concept of causal behavioural profiles provides a weaker behavioural consistency notion that can be computed efficiently using structural decomposition techniques for sound free-choice workflow systems if unstructured net fragments are acyclic or can be traced back to S- or T-nets.

We consider the following decision problems: PROOFNET: Given a multiplicative linear logic (MLL) proof structure, is it a proof net? ESSNET: Given an essential net (of an intuitionistic MLL sequent), is it correct? In this paper we show that linear-time algorithms for ESS-NET can be obtained by constructing the dominator tree of the input essential net. As a corollary, by showing that PROOFNET is linear-time reducible to ESSNET (by the trip translation), we obtain a linear-time algorithm for PROOFNET. We show further that these linear-time algorithms can be optimized to simple one-pass algorithms – each node of the input structure is visited at most once. As another application of dominator trees, we obtain lineartime algorithms for sequentializing proof nets (i.e. given a proof net, find a derivation for the underlying MLL sequent) and essential nets.

Abstract. The computation of dominators in a flowgraph has applications in program optimization, circuit testing, and other areas. Lengauer and Tarjan [17] 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 than the bit-vector algorithm even on graphs of moderate size. Recently Cooper et al. [9] have proposed a new, simple, tree-based iterative algorithm. Their experiments suggested that it was faster than the simple version of the Lengauer-Tarjan algorithm on graphs representing computer program control flow. Motivated by the work of Cooper et al., we present an experimental study comparing their algorithm (and some variants) with careful implementations of both versions of the Lengauer-Tarjan algorithm and with a new hybrid algorithm. Our results suggest that, although the performance of all the algorithms is similar, the most consistently fast are the simple Lengauer-Tarjan algorithm and the hybrid algorithm, and their advantage increases as the graph gets bigger or more complicated. 1

this report are heuristical in the way they try to conform to both the constraints of timing and resources. This will not always be obvious