Linear Layouts in Submodular Systems

Nagamochi, Hiroshi

doi:10.1007/978-3-642-35261-4_50

Cited by 15 publications

(16 citation statements)

References 22 publications

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“…To determine the pathwidth of an instance, we implemented the exact algorithm by Nagamochi [10]. The tests were carried out on a PC with CPU Intel Core i5-2500K 3.30GHz using chemical graphs generated from the chemical compounds in NCI database (http://cactus.nci.nih.gov/index.html).…”

Section: Resultsmentioning

confidence: 99%

“…In the third experiment, we use all 199,509 chemical graphs with at most 50 vertices in NCI database to try to compute their pathwidth under the time limit set to be 300 seconds, where we first apply our reductions to get smaller instances before we use the algorithm in [10] to compute the pathwidth, and the time includes the preprocessing time for our reduction method. Table 3 shows the distribution of the pathwidth of chemical graphs with at most 50 vertices which can be computed within 300 seconds, where we halt the computation when the pathwidth turns out to be at least 5.…”

Section: Distribution Of Pathwidth Over Chemical Graphs With At Most mentioning

confidence: 99%

“…Suchan et al [14] designed an algorithm that runs in 1.9657 n n O(1) time and space, and afterwards Kitsunai et al [9] gave an algorithm that runs in 1.89 n n O (1) time and space. Robertson and Seymour [13] led to a consequence of the graph minor theorem that for a fixed k there is a polynomial time algorithm that decides whether the pathwidth of a given graph is at most k. Nagamochi [10] proposed a branching algorithm for finding a linear layout with a bounded width that minimizes a given cost function, based on which it takes O(kmn 2k ) time and O(m + n) space to test whether the pathwidth of a given digraph with n vertices and m edges is at most k.…”

Section: Introductionmentioning

confidence: 99%

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Some Reduction Procedure for Computing Pathwidth of Undirected Graphs

Ikeda

Nagamochi

2015

IEICE Trans. Inf. & Syst.

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SUMMARYComputing an invariant of a graph such as treewidth and pathwidth is one of the fundamental problems in graph algorithms. In general, determining the pathwidth of a graph is NP-hard. In this paper, we propose several reduction methods for decreasing the instance size without changing the pathwidth, and implemented the methods together with an exact algorithm for computing pathwidth of graphs. Our experimental results show that the number of vertices in all chemical graphs in NCI database decreases by our reduction methods by 53.81% in average.

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Section: Resultsmentioning

confidence: 99%

Section: Distribution Of Pathwidth Over Chemical Graphs With At Most mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some Reduction Procedure for Computing Pathwidth of Undirected Graphs

Ikeda

Nagamochi

2015

IEICE Trans. Inf. & Syst.

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“…The directed path-width of a digraph G = (V, E) can be computed in time O( |E|·|V | 2d-pw(G) /(d-pw(G)−1)!) by [48] and in time O(d-pw(G) · |E| · |V | 2d-pw(G) ) by [52]. This leads to XP-algorithms for directed path-width w.r.t.…”

Section: Directed Path-widthmentioning

confidence: 99%

Comparing Linear Width Parameters for Directed Graphs

Gurski

Rehs

2019

Theory Comput Syst

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In this paper we introduce the linear clique-width, linear NLC-width, neighbourhood-width, and linear rank-width for directed graphs. We compare these parameters with each other as well as with the previously defined parameters directed path-width and directed cut-width. It turns out that the parameters directed linear clique-width, directed linear NLC-width, directed neighbourhood-width, and directed linear rank-width are equivalent in that sense, that all of these parameters can be upper bounded by each of the others. For the restriction to digraphs of bounded vertex degree directed path-width and directed cut-width are equivalent. Further for the restriction to semicomplete digraphs of bounded vertex degree all six mentioned width parameters are equivalent. We also show close relations of the measures to their undirected versions of the underlying undirected graphs, which allow us to show the hardness of computing the considered linear width parameters for directed graphs. Further we give first characterizations for directed graphs defined by parameters of small width.

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“…For arbitrary k, Miller and Sudborough [35] designed an algorithm running in O(n k 2 +3k+3 ) time. Moreover, Nagamochi [37] presented a framework for solving cutwidth-related graph problems in n O(k) time.…”

Section: 22 and 442]mentioning

confidence: 99%

Myhill–Nerode Methods for Hypergraphs

et al. 2015

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Abstract. We give an analog of the Myhill-Nerode methods from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems.• We provide an algorithm for testing whether a hypergraph has cutwidth at most k that runs in linear time for constant k. In terms of parameterized complexity theory, the problem is fixed-parameter linear parameterized by k.• We show that it is not expressible in monadic second-order logic whether a hypergraph has bounded (fractional, generalized) hypertree width. The proof leads us to conjecture that, in terms of parameterized complexity theory, these problems are W[1]-hard parameterized by the incidence treewidth (the treewidth of the incidence graph).Thus, in the form of the Myhill-Nerode theorem for hypergraphs, we obtain a method to derive linear-time algorithms and to obtain indicators for intractability for hypergraph problems parameterized by incidence treewidth.In an appendix, we point out an error and a fix to the proof of the MyhillNerode theorem for graphs in Downey and Fellow's book on parameterized complexity. * A preliminary version of this article appeared in the proceedings of ISAAC 2013 [44]. This extended and revised version contains the full proof details, more figures, and corollaries to make the application of the Myhill-Nerode theorem for hypergraphs easier in an algorithmic setting. Moreover, it provides a fix to the proof of the Myhill-Nerode theorem for graphs in the books of Downey and Fellows [14,15]

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Linear Layouts in Submodular Systems

Cited by 15 publications

References 22 publications

Some Reduction Procedure for Computing Pathwidth of Undirected Graphs

Some Reduction Procedure for Computing Pathwidth of Undirected Graphs

Comparing Linear Width Parameters for Directed Graphs

Myhill–Nerode Methods for Hypergraphs

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