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Heuristics for the Maximum Outerplanar Subgraph Problem

Timo Poranen
2005 Journal of Heuristics  
Determining the maximum outerplanar subgraph of a given graph is known to be an NP-complete problem.  ...  In the literature there are no earlier experiment on approximating the maximum outerplanar subgraph problem.  ...  Acknowledgments The author thanks the anonymous referees for their valuable comments.  ... 
doi:10.1007/s10732-005-6999-6 fatcat:64d2gevefnb75htnbtoau3paly

A simulated annealing algorithm for the maximum planar subgraph problem

Timo Poranen
2004 International Journal of Computer Mathematics  
The maximum planar subgraph problem (MPS) is defined as follows: given a graph G, find a largest planar subgraph of G.  ...  The first new algorithm still runs in the same time, produces outerplanar subgraphs, has at least the same performance ratio as the original algorithm, but in practice it finds larger planar subgraphs  ...  Acknowledgements The author thanks the anonymous referees for their valuable comments.  ... 
doi:10.1080/00207160410001684352 fatcat:lyb2sijmnzfidjwajjcq7z2tf4

Approximating the minimum hub cover problem on planar graphs

Belma Yelbay, Ş. İlker Birbil, Kerem Bülbül, Hasan Jamil
2015 Optimization Letters  
The problem, which is referred to as the minimum hub cover problem, has recently been introduced to the literature to improve query processing over large graph databases.  ...  Computational results also indicate that the efficacy of the decomposition-based heuristic in terms of solution quality is comparable to that of the approximation algorithm.  ...  However, the maximum optimality gaps of the decomposition-based heuristic are slightly larger than that of the approximation algorithm. values of k.  ... 
doi:10.1007/s11590-015-0876-5 fatcat:xzmopsaflrgjtdsl7nnridg2my

Isomorphic Subgraphs [chapter]

Sabine Bachl
1999 Lecture Notes in Computer Science  
We show that the Isomorphic Subgraphs problem is NP-hard for connected outerplanar graphs, and 2-connected planar graphs and is solvable in linear time when restricted to trees.  ...  For a given graph G the Isomorphic Subgraphs problem makes use of the second approach and tries to find the two largest disjoint isomorphic subgraphs in G.  ...  Brandenburg for his various and detailed comments and suggestions, particularly on the proof of Isomorphic Subgraphs of general graphs.  ... 
doi:10.1007/3-540-46648-7_30 fatcat:wiec3yfyk5agpeweik3zz3ybby

Beyond trees: MRF inference via outer-planar decomposition

Dhruv Batra, A. C. Gallagher, Devi Parikh, Tsuhan Chen
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
These are methods that decompose the given problem over a graph into tractable subproblems over subgraphs and then employ message passing over these subgraphs to merge the solutions of the subproblems  ...  Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g. trees), or approximate  ...  We thank Pedro Felzenszwalb for pointing out the connections between outer-planar graphs and k-trees, and Carlos Guestrin and Ramin Zabih for helpful discussions.  ... 
doi:10.1109/cvpr.2010.5539951 dblp:conf/cvpr/BatraGPC10 fatcat:zpodxtnqabbm7c6w5ozwgfq7qe

A polynomial-time maximum common subgraph algorithm for outerplanar graphs and its application to chemoinformatics

Leander Schietgat, Jan Ramon, Maurice Bruynooghe
2013 Annals of Mathematics and Artificial Intelligence  
In this article, we present a polynomial-time algorithm that computes a maximum common subgraph of two outerplanar graphs.  ...  Metrics for structured data have received an increasing interest in the machine learning community.  ...  Jan Ramon is supported by the ERC Starting Grant 240186 "MiGraNT" and the KU Leuven GOA project "Probabilistic  ... 
doi:10.1007/s10472-013-9335-0 fatcat:fvenicakhbe47n2eiubr7n5t6u

Approximation algorithms for weighted matching

Shankar M. Venkatesan
1987 Theoretical Computer Science  
Approximation algorithms are given for the maximum weighted matching problem in planar and other n-vertex graphs of genus g < n. For a planar graph, our approximation runs in O(min{n(  ...  Acknowledgment This paper is an extended and revised version of the results presented in [18] . The author thanks the referees for their helpful comments.  ...  The idea of approximating problems in P seems particularly justified for the important problem of finding a maximum weighted matching in an undirected graph with arbitrary weights on the edges [9] for  ... 
doi:10.1016/0304-3975(87)90022-3 fatcat:7z6dwfqo35g77j4xguv6e4wsz4

An Efficiently Computable Graph-Based Metric for the Classification of Small Molecules [chapter]

Leander Schietgat, Jan Ramon, Maurice Bruynooghe, Hendrik Blockeel
2008 Lecture Notes in Computer Science  
Representing the molecules as outerplanar graphs, a subclass within general graphs, and using the block-and-bridge preserving subgraph isomorphism, we define a metric and we present an algorithm for computing  ...  The application we focus on is drug discovery. Although graphs have become very popular for the representation of molecules, a lot of operations on graphs are NP-complete.  ...  Acknowledgements L.S. is supported by a PhD grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT).  ... 
doi:10.1007/978-3-540-88411-8_20 fatcat:qsa5h6bzbzgnjcmbdehdtwjzaq

A Fast Heuristic for Computing Geodesic Cores in Large Networks [article]

Florian Seiffarth, Tamás Horváth, Stefan Wrobel
2022 arXiv   pre-print
It generates a set of almost maximal outerplanar spanning subgraphs for the input graph, computes the geodesic closure in each of these graphs, and regards a node as an element of the convex hull if it  ...  belongs to the closed sets for at least a user specified number of outerplanar graphs.  ...  The algorithm solving Problem 1 for outerplanar graphs is given in Alg. 3.  ... 
arXiv:2206.07350v1 fatcat:2bt4rnjqhvbohfh3kojddcomla

Probabilistic satisfiability

George Georgakopoulos, Dimitris Kavvadias, Christos H Papadimitriou
1988 Journal of Complexity  
Since this problem is a generalization of the satisfiability problem for propositional calculus it is immediately NP-hard.  ...  We study the following computational problem proposed by Nils Nilsson: Several clauses (disjunctions of literals) are given, and for each clause the probability that the clause is true is specified.  ...  ACKNOWLEDGMENTS We thank Foto Afrati, Nils Nilsson, and John Tsitsiklis for helpful discussions on this and related problems. This research was partially supported by the National Science Foundation.  ... 
doi:10.1016/0885-064x(88)90006-4 fatcat:z247a553hnep7doewbmh6lc5aa

COMPARISON AND ENUMERATION OF CHEMICAL GRAPHS

Tatsuya Akutsu, Hiroshi Nagamochi
2013 Computational and Structural Biotechnology Journal  
We also discuss the relationship between the fifth problem and kernel functions for chemical compounds.  ...  In this review article, we overview several graph classes relevant to chemical compounds and the computational complexities of several fundamental problems for these graph classes.  ...  Acknowledgements This work was supported in part by Grant-in-Aid for Scientific Research (KAKENHI) no. 22240009 from JSPS, Japan. Citation  ... 
doi:10.5936/csbj.201302004 pmid:24688697 pmcid:PMC3962186 fatcat:lj6f3cmaybhunhcjr3662o3lry

Upper Domination: Complexity and Approximation [chapter]

Cristina Bazgan, Ljiljana Brankovic, Katrin Casel, Henning Fernau, Klaus Jansen, Kim-Manuel Klein, Michael Lampis, Mathieu Liedloff, Jérôme Monnot, Vangelis Th. Paschos
2016 Lecture Notes in Computer Science  
for Maximum Minimal Vertex Cover.  ...  We consider Upper Domination, the problem of finding a maximum cardinality minimal dominating set in a graph.  ...  Part of this research was supported by the DFG, grant FE 560/6-1.  ... 
doi:10.1007/978-3-319-44543-4_19 fatcat:yvj2hrr4jra6hn6krwqhmo2ygq

The complexity of finding the maximum spanning DAG and other restrictions for DAG parsing of natural language

Natalie Schluter
2015 Proceedings of the Fourth Joint Conference on Lexical and Computational Semantics  
Consideration of the decoding problem in natural language semantic dependency parsing as finding a maximum spanning DAG of a weighted directed graph carries many complexities.  ...  On the other hand, we show that under the restriction of projectivity, the problem has a straightforward O(n 3 ) algorithm.  ...  To our knowledge, approximability of finding a maximum weighted planar or outerplanar acyclic directed subgraph is still an open problem.  ... 
doi:10.18653/v1/s15-1031 dblp:conf/starsem/Schluter15 fatcat:tpmwn3fi75e2zll6zc7wzlsvti

The Maximum k-Differential Coloring Problem [article]

Michael Bekos, Stephen Kobourov, Michael Kaufmann, Sankar Veeramoni
2014 arXiv   pre-print
The same negative result holds for the ( 2n/3 , 2n-differential coloring problem, even in the case where the input graph is planar.  ...  Given an n-vertex graph G and two positive integers d,k ∈N, the (d,kn)-differential coloring problem asks for a coloring of the vertices of G (if one exists) with distinct numbers from 1 to kn (treated  ...  This is our main motivation for studying the maximum k-differential coloring problem for k > 1.  ... 
arXiv:1409.8133v2 fatcat:qxnv4t6qqfbznj3rsvwzolb3k4

The k-edge connected subgraph problem: Valid inequalities and Branch-and-Cut

F. Bendali, I. Diarrassouba, M. Didi Biha, A. R. Mahjoub, J. Mailfert
2007 2007 6th International Workshop on Design and Reliable Communication Networks  
In this paper we consider the k-edge connected subgraph problem from a polyhedral point of view.  ...  We introduce further classes of valid inequalities for the associated polytope, and describe sufficient conditions for these inequalities to be facet defining.  ...  We fixed the maximum CPU time to 5 hours. The test problems were obtained by taking TSP test problems from the TSPLIB library [36] .  ... 
doi:10.1109/drcn.2007.4762290 fatcat:x3okqnpdfvcdfhrblfksbbbytq
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