A Polynomial-Time Algorithm for Computing the Maximum Common Connected Edge Subgraph of Outerplanar Graphs of Bounded Degree

Akutsu, Tatsuya; Tamura, Takeyuki

doi:10.3390/a6010119

Cited by 15 publications

(16 citation statements)

References 22 publications

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“…Given a bipartite graph G with edge weights w : E(G) → R, the weighted maximal matching problem asks for a matching M ⊆ E in G such that the weight w(M ) = e∈M w(e) is maximal. 1 An isomorphism between two graphs G and H is a bijection ϕ : Figure 1. The above definitions can be naturally extended to graphs with vertex and edge labels, where an isomorphism must preserve labels and the weight function may depend on the labels.…”

Section: Preliminariesmentioning

confidence: 99%

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A note on block-and-bridge preserving maximum common subgraph algorithms for outerplanar graphs

Kriege¹,

Droschinsky²,

Mutzel³

2018

JGAA

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Schietgat, Ramon and Bruynooghe [18] proposed a polynomial-time algorithm for computing a maximum common subgraph under the block-and-bridge preserving subgraph isomorphism (BBP-MCS) for outerplanar graphs. We show that the article contains the following errors: (i) The running time of the presented approach is claimed to be O(n 2.5 ) for two graphs of order n. We show that the algorithm of the authors allows no better bound than O(n 4 ) when using state-of-the-art general purpose methods to solve the matching instances arising as subproblems. This is even true for the special case, where both input graphs are trees.(ii) The article suggests that the dissimilarity measure derived from BBP-MCS is a metric. We show that the triangle inequality is not always satisfied and, hence, it is not a metric. Therefore, the dissimilarity measure should not be used in combination with techniques that rely on or exploit the triangle inequality in any way.Where possible, we give hints on techniques that are suitable to improve the algorithm.

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Section: Preliminariesmentioning

confidence: 99%

“…The maximum common subgraph problem in outerplanar graphs of bounded degree can be solved in polynomial time [1]. Although molecular graph have bounded degree and are often outerplanar, the algorithm has a high running time and is probably not suitable for practical use.…”

Section: Introductionmentioning

confidence: 99%

A note on block-and-bridge preserving maximum common subgraph algorithms for outerplanar graphs

Kriege¹,

Droschinsky²,

Mutzel³

2018

JGAA

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“…Adding the connectedness requirement makes certain special cases solvable in polynomial time, including outerplanar graphs of bounded degree [1] and trees [14], but the general case remains NP-hard. As illustrated in Fig.…”

Section: Finding Maximum Common Connected Subgraphsmentioning

confidence: 99%

Clique and Constraint Models for Maximum Common (Connected) Subgraph Problems

McCreesh¹,

Ndiaye²,

Prosser³

et al. 2016

Lecture Notes in Computer Science

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Abstract. The maximum common subgraph problem is to find the largest subgraph common to two given graphs. This problem can be solved either by constraint-based search, or by reduction to the maximum clique problem. We evaluate these two models using modern algorithms, and see that the best choice depends mainly upon whether the graphs have labelled edges. We also study a variant of this problem where the subgraph is required to be connected. We introduce a filtering algorithm for this property and show that it may be combined with a restricted branching technique for the constraint-based approach. We show how to implement a similar branching technique in clique-inspired algorithms. Finally, we experimentally compare approaches for the connected version, and see again that the best choice depends on whether graphs have labels.

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“…In the case of the maximum common subgraph, the corresponding decision version is NP-complete as it solves the subgraph isomorphism problem. The problem remains NP-hard, even on restricted graph classes such as outerplanar graphs, and becomes polynomial only if the degree is bounded or for trees [27]. The problem is difficult to approximate (MAX-SNP hard) even within a polynomial factor [19], and is W [1]-hard when parameterized by the treewidth of the input graphs [16].…”

Section: Introductionmentioning

confidence: 99%