Finding Dominators in Practice

Georgiadis, Loukas; Werneck, Renato F.; Tarjan, Robert E.; Triantafyllis, Spyridon; August, David I.

doi:10.1007/978-3-540-30140-0_60

Cited by 34 publications

(48 citation statements)

References 16 publications

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“…A flow graph is a digraph with a distinguished start vertex s such that every vertex is reachable from s. We let G s (resp., G We say that a vertex v = s is a nontrivial dominator of G s if d(w) = v for some vertex w. Similarly, vertex v is a nontrivial dominator of w in G s if v dominates w and v ∈ {s, w}. If v is a nontrivial dominator of w in both G s and G R s , then we say that v is a common nontrivial dominator of w. Dominators are a central tool in program optimization and code generation [9], and have applications in other diverse areas [14]. The dominator tree can be computed in linear time [2,7].…”

Section: Preliminaries and Notationmentioning

confidence: 99%

Computing Critical Nodes in Directed Graphs

Paudel

Georgiadis

Italiano

2017

2017 Proceedings of the Ninteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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We consider the critical node detection problem (CNDP) in directed graphs. Given a directed graph G and a parameter k, we wish to remove a subset S of at most k vertices of G such that the residual graph G \ S has minimum pairwise strong connectivity. This problem is NP-hard, and thus we are interested in practical heuristics. We present a sophisticated linear-time algorithm for the k = 1 case, and, based on this algorithm, give an efficient heuristic for the general case. Then, we conduct a thorough experimental evaluation of various heuristics for CNDP. Our experimental results suggest that our heuristic performs very well in practice, both in terms of running time and of solution quality.

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Section: Preliminaries and Notationmentioning

confidence: 99%

Computing Critical Nodes in Directed Graphs

Paudel

Georgiadis

Italiano

2017

2017 Proceedings of the Ninteenth Workshop on Algorithm Engineering and Experiments (ALENEX)

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“…But this sophisticated algorithm relies on depth-first search (DFS) spanning tree of the CFG with elaborate path compression and tree balancing techniques to achieve a stunning near-linear complexity. We refer the interested reader to [16] for a more complete survey of the numerous algorithms proposed so far in the literature, and to [10] for a thorough experimental study comparing the leading algorithms.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Validating Dominator Trees for a Fast, Verified Dominance Test

Blazy

Demange

Pichardie

2015

Interactive Theorem Proving

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The problem of computing dominators in a control flow graph is central to numerous modern compiler optimizations. Many efficient algorithms have been proposed in the litterature, but mechanizing the correctness of the most sophisticated algorithms is still considered as too hard problems, and to this date, verified compilers use less optimized implementations. In contrast, production compilers, like GCC or LLVM, implement the classic, efficient Lengauer-Tarjan algorithm [12], to compute dominator trees. And subsequent optimization phases can then determine whether a CFG node dominates another node in constant time by using their respective depth-first search numbers in the dominator tree. In this work, we aim at integrating such techniques in verified compilers. We present a formally verified validator of untrusted dominator trees, on top of which we implement and prove correct a fast dominance test following these principles. We conduct our formal development in the Coq proof assistant, and integrate it in the middle-end of the CompCertSSA verified compiler. We also provide experimental results showing performance improvement over previous formalizations.

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“…To study the asymptotic complexity, Figure 11 shows the result of graphs that elicit the worst-case behavior used in [8]. On average, CHK is 86.59 times slower than LT.…”

Section: Performance Evaluationmentioning

confidence: 99%

“…Moreover, LT explictly creates dominator trees that provide convenient data structures for compilers whereas AC needs an additional tree construction algorithm with more overhead. The Cooper-Harvey-Kennedy algorithm [5] (CHK), extended from AC with careful engineering, runs nearly as fast as LT in common cases [5,8], but is still simple to implement and reason about. Moreover, CHK generates dominator trees implicitly, and provides a faster tree construction algorithm.…”

Section: Instantiationsmentioning

confidence: 99%

Mechanized Verification of Computing Dominators for Formalizing Compilers

Zhao

Zdancewic

2012

Certified Programs and Proofs

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Abstract. One prerequisite to the formal verification of modern compilers is to formalize computing dominators, which enable SSA forms, advanced optimizations, and analysis. This paper provides an abstract specification of dominance analysis that is sufficient for formalizing modern compilers; it describes a certified implementation and instance of the specification that is simple to design and reason about, and also reasonably efficient. The paper also presents applications of dominance analysis: an SSA-form type checker, verifying SSA-based optimizations, and constructing dominator trees. This development is a part of the Vellvm project. All proofs and implementation have been carried out in Coq.

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Finding Dominators in Practice

Cited by 34 publications

References 16 publications

Computing Critical Nodes in Directed Graphs

Computing Critical Nodes in Directed Graphs

Validating Dominator Trees for a Fast, Verified Dominance Test

Mechanized Verification of Computing Dominators for Formalizing Compilers

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