Experimental Study of FPT Algorithms for the Directed Feedback Vertex Set Problem

Fleischer, Rudolf; Wu, Xi; Yuan, Liwei

doi:10.1007/978-3-642-04128-0_55

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…MAIN CONTRIBUTIONS AND OUTLINE 3 take up ideas from FPT or kernelization theory, e.g. for independent sets (or equivalently vertex cover) [27,35,44,97,98,122], for cut tree construction [5], for treewidth computations [16,117,183], for the feedback vertex set problem [62,114], for the dominating set problem [2], for the maximum cut problem [57], for the cluster editing problem [23], and the matching problem [116]. In this dissertation, we make heavy use of data reduction techniques to improve the performance of algorithms for the minimum cut problem and the multiterminal cut problem.…”

Section: Motivationmentioning

confidence: 99%

Practical Minimum Cut Algorithms

Henzinger

Noe

Schulz

et al. 2018

ACM J. Exp. Algorithmics

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The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. Here, we introduce a linear-time algorithm to compute near-minimum cuts. Our algorithm is based on cluster contraction using label propagation and Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both sequential and shared-memory parallel implementations of our algorithm. Extensive experiments on both real-world and generated instances show that our algorithm finds the optimal cut on nearly all instances significantly faster than other state-of-the-art algorithms while our error rate is lower than that of other heuristic algorithms. In addition, our parallel algorithm shows good scalability.

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Section: Motivationmentioning

confidence: 99%

Practical Minimum Cut Algorithms

Henzinger

Noe

Schulz

et al. 2018

ACM J. Exp. Algorithmics

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“…The DFVS problem corresponds to C-Deletion where C is the set of directed acyclic graphs and forb(C) is the set of directed cycles. The preconditions of Theorem 3.2 follow from known results, see for instance the work of Fleischer et al [22], we repeat it for completeness. Consider any directed graph D and vertex v ∈ V (D).…”

Section: Claim 34 ([5 Page 67]mentioning

confidence: 88%

Search-Space Reduction via Essential Vertices

Bumpus¹,

Jansen²,

Kroon³

2022

Preprint

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We investigate preprocessing for vertex-subset problems on graphs. While the notion of kernelization, originating in parameterized complexity theory, is a formalization of provably effective preprocessing aimed at reducing the total instance size, our focus is on finding a non-empty vertex set that belongs to an optimal solution. This decreases the size of the remaining part of the solution which still has to be found, and therefore shrinks the search space of fixed-parameter tractable algorithms for parameterizations based on the solution size. We introduce the notion of a c-essential vertex as one that is contained in all c-approximate solutions. For several classic combinatorial problems such as Odd Cycle Transversal and Directed Feedback Vertex Set, we show that under mild conditions a polynomial-time preprocessing algorithm can find a subset of an optimal solution that contains all 2-essential vertices, by exploiting packing/covering duality. This leads to FPT algorithms to solve these problems where the exponential term in the running time depends only on the number of non-essential vertices in the solution.

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“…The general interest of the kernelization process is the reduction of the size of the input given to an algorithm which is not polynomial in time (in most cases): the graph is being "compressed". As we work in the directed case, we used the kernelization technique applied to the directed FVS [8], following the four first rules of the method. The two first rules imply a simple digraph (no self-loop, no multiple arcs), the third one removes isolated nodes (degree equal to zero), and the last one removes the chained nodes, by removing nodes from the digraph while it contains nodes with only one outgoing or incoming arc.…”

Section: Digraph Kernelizationmentioning

confidence: 99%

Core Decomposition in Directed Networks: Kernelization and Strong Connectivity

Levorato

2014

Complex Networks V

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In this paper, we propose a method allowing decomposition of directed networks into cores, which final objective is the detection of communities. We based our approach on the fact that a community should be composed of elements having communication in both directions. Therefore, we propose a method based on digraph kernelization and strongly p-connected components. By identifying cores, one can use based-centers clustering methods to generate full communities. Some experiments have been made on three real-world networks, and have been evaluated using the V-Measure, allowing a more precise analysis through its two sub-measures: homogeneity and completeness. Our work proposes different directions about the use of kernelization into structure analysis, and strong connectivity concept as an alternative to modularity optimization.

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Experimental Study of FPT Algorithms for the Directed Feedback Vertex Set Problem

Cited by 9 publications

References 10 publications

Practical Minimum Cut Algorithms

Practical Minimum Cut Algorithms

Search-Space Reduction via Essential Vertices

Core Decomposition in Directed Networks: Kernelization and Strong Connectivity

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