Cycles through specified vertices in triangle-free graphs

Paulusma, Daniël; Yoshimoto, Kiyoshi

doi:10.7151/dmgt.1354

Cited by 4 publications

(2 citation statements)

References 11 publications

(10 reference statements)

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“…After calling Algorithm 3, the arc 3, 4 is deleted. Repeat the above process, cycles (5,6,7,10) and (1,4,5) are detected and removed, and then the graph is cycle-free. In one word, Algorithm 4 can find 3 cycles in Figure 1.…”

Section: An Examplementioning

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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Section: An Examplementioning

confidence: 99%

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

et al. 2017

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“…Since a longest cycle does not always contain all large degree vertices, it would be also an interesting problem to ask whether there is a (longest) cycle containing special vertices (all large degree vertices from some degree). For examples that there is a (longest) cycle contains some special vertices in a graph, see [1], [7], [11] and [12], [14]; for paths, see [8], [13], for digraphs, see [6].…”

Section: Introductionmentioning

confidence: 99%

Large degree vertices in longest cycles of graphs II

Xiong

Yin

2019

ejgta

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Fast parallel algorithms for finding elementary circuits of a directed graph: a GPU-based approach

Benachour

Yahiaoui²,

Baz³

et al. 2022

J Supercomput

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Circuits in a graph are interesting structures and identifying them is of an important relevance for many applications. However, enumerating circuits is known to be a difficult problem, since their number can grow exponentially. In this paper, we propose fast parallel approaches for enumerating elementary circuits of a directed graphs based on Graphics Processing Unit (GPU). Our algorithms are based on a massive exploration of the graph in a Breadth First Search (BFS) strategy. Algorithm V-FEC explores the graph starting from different vertices simultaneously. To further reduce the search space, we present T-FEC, another algorithm that uses triplets as an initial set to start exploring. To the best of our knowledge, those are the first parallel GPU-based algorithms for finding all circuits of a given graph. The evaluation results show that the proposed approaches achieves up to 190x speed-up over Johnson's algorithm, one of the most efficient sequential algorithms for finding circuits.

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Cycles through specified vertices in triangle-free graphs

Cited by 4 publications

References 11 publications

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

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

Large degree vertices in longest cycles of graphs II

Fast parallel algorithms for finding elementary circuits of a directed graph: a GPU-based approach

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