Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth

Asadi, Ali Al; Chatterjee, Krishnendu; Goharshady, Amir Kafshdar; Mohammadi, Kiarash; Pavlogiannis, Andreas

doi:10.1007/978-3-030-59152-6_14

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…The theoretical bound of [78] does not apply to Java, but the work [44] showed that the treewidth of control-flow graphs in real-world Java programs is also bounded. This bounded-treewidth property has been used in a variety of static analysis and compiler optimization tasks to speed up the underlying algorithms [25,62,3,27,36,26,20,23,5,38,2]. Nevertheless, one can theoretically construct pathological examples with high treewidth.…”

Section: Treewidth and Treedepthmentioning

confidence: 99%

Efficient Interprocedural Data-Flow Analysis Using Treedepth and Treewidth

Goharshady

Zaher

2023

Lecture Notes in Computer Science

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We consider interprocedural data-flow analysis as formalized by the standard IFDS framework, which can express many widelyused static analyses such as reaching definitions, live variables, and nullpointer. We focus on the well-studied on-demand setting in which queries arrive one-by-one in a stream and each query should be answered as fast as possible. While the classical IFDS algorithm provides a polynomialtime solution for this problem, it is not scalable in practice. More specifically, it will either require a quadratic-time preprocessing phase or takes linear time per query, both of which are untenable for modern huge codebases with hundreds of thousands of lines. Previous works have already shown that parameterizing the problem by the treewidth of the program's control-flow graph is promising and can lead to significant gains in efficiency. Unfortunately, these results were only applicable to the limited special case of same-context queries. In this work, we obtain significant speedups for the general case of ondemand IFDS with queries that are not necessarily same-context. This is achieved by exploiting a new graph sparsity parameter, namely the treedepth of the program's call graph. Our approach is the first to exploit the sparsity of control-flow graphs and call graphs at the same time and parameterize by both the treewidth and the treedepth. We obtain an algorithm with a linear preprocessing phase that can answer each query in constant time wrt the size of the input. Finally, our experimental results demonstrate that our approach significantly outperforms the classical IFDS and its on-demand variant.

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Section: Treewidth and Treedepthmentioning

confidence: 99%

Efficient Interprocedural Data-Flow Analysis Using Treedepth and Treewidth

Goharshady

Zaher

2023

Lecture Notes in Computer Science

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“…Several NP-hard problems for graphs, for example the 3coloring problem, are in P for graphs with bounded tree width [6]. Faster algorithms for standard problems in probabilistic model checking were proposed for systems of small tree width [3,11]. Algorithms for non-probabilistic quantitative verification problems on models with low tree width were considered in [10].…”

Section: Introductionmentioning

confidence: 99%

Witnessing Subsystems for Probabilistic Systems with Low Tree Width

Jantsch

Piribauer

Baier

2021

Electron. Proc. Theor. Comput. Sci.

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A standard way of justifying that a certain probabilistic property holds in a system is to provide a witnessing subsystem (also called critical subsystem) for the property. Computing minimal witnessing subsystems is NP-hard already for acyclic Markov chains, but can be done in polynomial time for Markov chains whose underlying graph is a tree. This paper considers the problem for probabilistic systems that are similar to trees or paths. It introduces the parameters directed tree-partition width (dtpw) and directed path-partition width (dppw) and shows that computing minimal witnesses remains NP-hard for Markov chains with bounded dppw (and hence also for Markov chains with bounded dtpw). By observing that graphs of bounded dtpw have bounded width with respect to all known tree similarity measures for directed graphs, the hardness result carries over to these other tree similarity measures. Technically, the reduction proceeds via the conceptually simpler matrix-pair chain problem, which is introduced and shown to be NP-complete for nonnegative matrices of fixed dimension. Furthermore, an algorithm which aims to utilise a given directed tree partition of the system to compute a minimal witnessing subsystem is described. It enumerates partial subsystems for the blocks of the partition along the tree order, and keeps only necessary ones. A preliminary experimental analysis shows that it outperforms other approaches on certain benchmarks which have directed tree partitions of small width.

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“…The definition of access hypergraphs provided here is a bit different from[19] since we allow our hyperedges to include the same vertex more than once. However, this difference does not affect the treewidth 3. Adjacent vertices need not necessarily have different colors.…”

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confidence: 99%

Efficient approximations for cache-conscious data placement

Ahmadi

Daliri

Goharshady

et al. 2022

Proceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation

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There is a huge and growing gap between the speed of accesses to data stored in main memory vs cache. Thus, cache misses account for a significant portion of runtime overhead in virtually every program and minimizing them has been an active research topic for decades. The primary and most classical formal model for this problem is that of Cacheconscious Data Placement (CDP): given a commutative cache with constant capacity 𝑘 and a sequence Σ of accesses to data elements, the goal is to map each data element to a cache line such that the total number of cache misses over Σ is minimized. Note that we are considering an offline singlethreaded setting in which Σ is known a priori. CDP has been widely studied since the 1990s. In POPL 2002, Petrank and Rawitz proved a notoriously strong hardness result: They showed that for every 𝑘 ≥ 3, CDP is not only NP-hard but also hard-to-approximate within any non-trivial factor unless P = NP. As such, all subsequent works gave up on theoretical improvements and instead focused on heuristic algorithms with no theoretical guarantees.In this work, we present the first-ever positive theoretical result for CDP. The fundamental idea behind our approach is that real-world instances of the problem have specific structural properties that can be exploited to obtain efficient

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Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth

Cited by 6 publications

References 28 publications

Efficient Interprocedural Data-Flow Analysis Using Treedepth and Treewidth

Efficient Interprocedural Data-Flow Analysis Using Treedepth and Treewidth

Witnessing Subsystems for Probabilistic Systems with Low Tree Width

Efficient approximations for cache-conscious data placement

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