A dynamic topological sort algorithm for directed acyclic graphs

Pearce, David J.

doi:10.1145/1187436.1210590

Cited by 55 publications

(42 citation statements)

References 28 publications

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“…Syntax Interestingly, the self-adjusting DFS program exhibits algorithmic and asymptotic complexity behavior similar to previously proposed algorithms for topological sorting of incrementally changing graphs, for example that by Pearce and Kelly [20]. The main difference compared to their work is, of course, that we obtained our code by simply annotating a standard, non-adjusting version of DFS.…”

Section: Programming With "Mutable Modifiables"mentioning

confidence: 83%

Imperative self-adjusting computation

Acar

Ahmed

Blume

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Recent work on self-adjusting computation showed how to systematically write programs that respond efficiently to incremental changes in their inputs. The idea is to represent changeable data using modifiable references, i.e., a special data structure that keeps track of dependencies between read and write-operations, and to let computations construct traces that later, after changes have occurred, can drive a change propagation algorithm. The approach has been shown to be effective for a variety of algorithmic problems, including some for which ad-hoc solutions had previously remained elusive.All previous work on self-adjusting computation, however, relied on a purely functional programming model. In this paper, we show that it is possible to remove this limitation and support modifiable references that can be written multiple times. We formalize this using a language AIL for which we define evaluation and change-propagation semantics. AIL closely resembles a traditional higher-order imperative programming language. For AIL we state and prove consistency, i.e., the property that although the semantics is inherently non-deterministic, different evaluation paths will still give observationally equivalent results. In the imperative setting where pointer graphs in the store can form cycles, our previous proof techniques do not apply. Instead, we make use of a novel form of a step-indexed logical relation that handles modifiable references.We show that AIL can be realized efficiently by describing implementation strategies whose overhead is provably constant-time per primitive. When the number of reads and writes per modifiable is bounded by a constant, we can show that change propagation becomes as efficient as it was in the pure case. The general case incurs a slowdown that is logarithmic in the maximum number of such operations. We use DFS and related algorithms on graphs as our running examples and prove that they respond to insertions and deletions of edges efficiently.

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Section: Programming With "Mutable Modifiables"mentioning

confidence: 83%

Imperative self-adjusting computation

Acar

Ahmed

Blume

2008

Proceedings of the 35th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…Many algorithms developed [10] to get topological sequence of a graph. The primary applications or Real word applications are instruction scheduling, ordering of formula cell evaluation when re-computing formula values in spreadsheets, logic synthesis, determining the order of compilation tasks to perform in make files, data serialization, and resolving symbol dependencies in linkers.…”

Section: B Topological Sortmentioning

confidence: 99%

Performance Analysis of a System that Identifies the Parallel Modules through Program Dependence Graph

Makka¹,

Sagar²

2017

IJISA

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Abstract-We have proposed a new approach to identify segments, which can be executed simultaneously, or coextending to achieve high computational speed with optimized utilization of available resources. Our suggested approach is divided into four modules. In first module we have represented a program segment using Abstract Syntax Tree (AST) along with an algorithm for constructing AST and in second module, this AST has been converted into Program Dependence Graph (PDG), the detailed approach has been described in section II, The process of construction of PDG is divided into two steps: First we construct a Control Dependence Graph (CDG, In second step reachability definition algorithm has been used to identify data dependencies between the various modules of a program by constructing Data Dependence Graph (DDG). In third module an algorithm is suggested to identify parallel modules, i.e., the modules that can be executed simultaneously in the section III and in fourth module performance analysis is discussed through our approach along with the computation of time complexity and its comparison with sequential approach is demonstrated in a pictorial form.

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“…Er [6] proposed a new topological sorting algorithm using the parallel computation approach. David [7] presented a new algorithm for the problem of maintaining the topological order of a DAG [8] in the presence of edge insertions and deletions. In [9], Deepak et al [10] presented a simple algorithm, which maintained the topological order of a DAG under an online edge insertion sequence in O(n2.75).For dense DAGs, this was an improvement over the previous best result.…”

Section: Introductionmentioning

confidence: 99%

“…An I/O-efficient algorithm for topologically sorting directed acyclic graphs was proposed in [11] and the algorithm was extremely inefficient and performs O(n• sort(m)) I/Os in the worst case but achieved good performance in practice. David [12] improved the previous algorithm in [7], by only recomputing those region(s) of order affected by the inserted edges to maintain the topological order. Katriel and Bodlaender studied online algorithms to maintain a topological ordering of a directed acyclic graph, it is optimal that the algorithm was implemented to run in O(n log n) time on trees [13].…”

Section: Introductionmentioning

confidence: 99%

Study on a Multi-Hierarchy Topological Sort Algorithm for Automatic Calculation

Zhao²,

Li³

et al. 2017

IJMUE

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Topological sort algorithm (Toposort) is widely used for practical problems. However, standard toposort don't solve the automatic calculation of formula problem (ACFP) directly. To gain the feasible topological order of ACFP, this paper puts forward a modified algorithm based toposort ,which models for ACFP using directed acyclic graph (DAG) firstly, and then puts the 0 in-degree formula nodes into a level list in execution process, lastly decreases the in-degree of other formula nodes ,whose parameters is correlate to the 0 in-degree nodes and in-degree

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A dynamic topological sort algorithm for directed acyclic graphs

Cited by 55 publications

References 28 publications

Imperative self-adjusting computation

Imperative self-adjusting computation

Performance Analysis of a System that Identifies the Parallel Modules through Program Dependence Graph

Study on a Multi-Hierarchy Topological Sort Algorithm for Automatic Calculation

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