A New Approach to Incremental Cycle Detection and Related Problems

Bender, Michael A.; Fineman, Jeremy T.; Gilbert, Seth; Tarjan, Robert E.

doi:10.1145/2756553

Cited by 48 publications

(40 citation statements)

References 28 publications

(31 reference statements)

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“…Hence, the naive approach in which after every update we simply recompute everything from scratch yields a O(nm + m 2 ) total update time. The problems of the incremental cycle detection and topological order have been extensively studied in the last three decades [3,19,21,15,18,2,1,16,8,4,5,6]. Marchetti-Spaccamela et al [19] obtained algorithms for these problems in O(nm) total update time.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Incremental Topological Sort and Cycle Detection in Expected Total Time

Bernstein

Chechik

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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In the incremental cycle detection problem edges are inserted to a directed graph (initially empty) and the algorithm has to report once a directed cycle is formed in the graph. A closely related problem to the incremental cycle detection is that of the incremental topological sort problem, in which edges are inserted to an acyclic graph and the algorithm has to maintain a valid topological sort on the vertices at all times.Both incremental cycle detection and incremental topological sort have a long history. The state of the art is a recent breakthrough of Bender, Fineman, Gilbert and Tarjan [TALG 2016], with two different algorithms with respective total update times ofÕ(n 2 ) and O(m · min{m 1/2 , n 2/3 }). The two algorithms work for both incremental cycle detection and incremental topological sort.In this paper we introduce a novel technique that allows us to improve upon the state of the art for a wide range of graph sparsity. Our algorithms has a total expected update time ofÕ(m √ n) for both the incremental cycle detection and the topological sort problems.

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Section: Introductionmentioning

confidence: 99%

“…In a breakthrough result Bender, Fineman, Gilbert and Tarjan [5] presented two different algorithms, with total update time of O(n 2 log n) and O(m · min{m 1/2 , n 2/3 }), respectively. Despite previous attempts, for sparse graphs no better than O(m 3/2 ) total update time algorithm was found.…”

Section: Introductionmentioning

confidence: 99%

Incremental Topological Sort and Cycle Detection in Expected Total Time

Bernstein

Chechik

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…The first for loop (lines 3-7) finds the cycle weight. The second for loop (lines [8][9][10][11][12][13][14][15][16][17][18][19][20] decreases all of the arc weights of C by w C . If the weight of an arc becomes 0, delete this arc (line 11).…”

Section: Algorithm 4 Detect Cycles Of a Weighted Directed Graphmentioning

confidence: 99%

A Multi-Threading Algorithm to Detect and Remove Cycles in Vertex- and Arc-Weighted Digraph

et al. 2017

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Abstract:A graph is a very important structure to describe many applications in the real world. In many applications, such as dependency graphs and debt graphs, it is an important problem to find and remove cycles to make these graphs be cycle-free. The common algorithm often leads to an out-of-memory exception in commodity personal computer, and it cannot leverage the advantage of multicore computers. This paper introduces a new problem, cycle detection and removal with vertex priority. It proposes a multithreading iterative algorithm to solve this problem for large-scale graphs on personal computers. The algorithm includes three main steps: simplification to decrease the scale of graph, calculation of strongly connected components, and cycle detection and removal according to a pre-defined priority in parallel. This algorithm avoids the out-of-memory exception by simplification and iteration, and it leverages the advantage of multicore computers by multithreading parallelism. Five different versions of the proposed algorithm are compared by experiments, and the results show that the parallel iterative algorithm outperforms the others, and simplification can effectively improve the algorithm's performance.

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“…To ensure the correctness of FastIDC, negative cycles had to be detected. The CCGraph was introduced for this purpose [10], and was updated using a fast but complex incremental topological ordering algorithm [1]. EIDC additionally needs to keep track of the transitive closure of all negative edges.…”

Section: Lemma 3 (Finished Lemma)mentioning

confidence: 99%

Efficient processing of simple temporal networks with uncertainty: algorithms for dynamic controllability verification

2015

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Temporal formalisms are essential for reasoning about actions that are carried out over time. The exact durations of such actions are generally hard to predict. In temporal planning, the resulting uncertainty is often worked around by only considering upper bounds on durations, with the assumption that when an action happens to be executed more quickly, the plan will still succeed. However, this assumption is often false: If we finish cooking too early, the dinner will be cold before everyone is ready to eat.Using Simple Temporal Networks with Uncertainty (STNU), a planner can correctly take both lower and upper duration bounds into account. It must then verify that the plans it generates are executable regardless of the actual outcomes of the uncertain durations. This is captured by the property of dynamic controllability (DC), which should be verified incrementally during plan generation.Recently a new incremental algorithm for verifying dynamic controllability was proposed: EfficientIDC, which can verify if an STNU that is DC remains DC after the addition or tightening of a constraint (corresponding to a new action being added to a plan). The algorithm was shown to have a worst case complexity of O(n 4 ) for each addition or tightening. This can be amortized over the construction of a whole STNU for an amortized complexity in O(n 3 ). In this paper we improve the EfficientIDC algorithm in a way that prevents it from having to reprocess nodes. This improvement leads to a lower worst case complexity in O(n 3 ).

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A New Approach to Incremental Cycle Detection and Related Problems

Cited by 48 publications

References 28 publications

Incremental Topological Sort and Cycle Detection in Expected Total Time

Incremental Topological Sort and Cycle Detection in Expected Total Time

A Multi-Threading Algorithm to Detect and Remove Cycles in Vertex- and Arc-Weighted Digraph

Efficient processing of simple temporal networks with uncertainty: algorithms for dynamic controllability verification

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