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Fast detection and display of symmetry in outerplanar graphs

Joseph Manning, Mikhail J. Atallah
1992 Discrete Applied Mathematics  
These results are then expanded to obtain algorithms for the detection and display of outerplanar axial and rotational symmetry in the entire class of outerplanar graphs.  ...  All algorithms run in both time and space which are linear in the size of the graph, and hence are optimal to within a constant factor.  ...  The actual encoding of G resembles that used in [6] for an outerplanar isomorphism test.  ... 
doi:10.1016/0166-218x(92)90112-n fatcat:gpzavtpif5hi7nzh362q6dvu7q

Page 5120 of Mathematical Reviews Vol. , Issue 911 [page]

1991 Mathematical Reviews  
parallel algorithms for testing isomorphism of trees and outerplanar graphs.  ...  This gives the first optimal parallel algorithm for isomorphism testing for a nontrivial class of graphs. We also give an optimal parallel algorithm for the equivalence of expressions.  ... 

Approximating the minimum hub cover problem on planar graphs

Belma Yelbay, Ş. İlker Birbil, Kerem Bülbül, Hasan Jamil
2015 Optimization Letters  
Our algorithm is based on a well-known graph decomposition technique that partitions the graph into a set of outerplanar graphs and provides an approximate solution with a proven performance ratio.  ...  We study an approximation algorithm with a performance guarantee to solve a new NP-hard optimization problem on planar graphs.  ...  Let S i j be a (k + 1)-outerplanar graph induced by levels jk + i to ( j + 1)k + i andS i j is the optimal solution of S i j .  ... 
doi:10.1007/s11590-015-0876-5 fatcat:xzmopsaflrgjtdsl7nnridg2my

Page 3822 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
“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.  ...  as well as linear time algorithms for classical optimization problems on split-perfect graphs based on the primeval decompo- sition of graphs.  ... 

Linear-time recognition of map graphs with outerplanar witness

Matthias Mnich, Ignaz Rutter, Jens M. Schmidt
2018 Discrete Optimization  
However, the run time of this algorithm is estimated to be Ω(n 120 ) for n-vertex graphs, and a full description of its details remains unpublished.  ...  We give a new and purely combinatorial algorithm that decides whether a graph G is a map graph having an outerplanar witness W .  ...  Thus, every parallel P -node in the SPQR tree has at most three parallel edges (and at least three by definition of SPQR trees): two virtual ones and one edge from G. 5:11 For (ii), observe that the  ... 
doi:10.1016/j.disopt.2017.12.002 fatcat:wtihkskgpzcabhylljn5rgxju4

Hammock-on-ears decomposition: A technique for the efficient parallel solution of shortest paths and other problems [chapter]

Dimitris Kavvadias, Grammati E. Pantziou, Paul G. Spirakis, Christos D. Zaroliagis
1994 Lecture Notes in Computer Science  
We i m p r o ve previous bounds for certain instances of shortest paths and related problems, in this class of graphs.  ...  We s h o w h o w to decompose e ciently in parallel any graph int o a n umber,~ , o f outerplanar subgraphs (called hammocks) satisfying certain separator properties.  ...  There are certain classes of graphs for which the value of~ is small. Examples are: outerplanar graphs, graphs which satisfy the k-interval property 15] and graphs with genus o(n).  ... 
doi:10.1007/3-540-58338-6_93 fatcat:jvnczhs265ditkcurk666tlddy

Graph-based data mining for biological applications

Leander Schietgat
2011 AI Communications  
Motivated by the fact that the majority of molecules can be represented as outerplanar graphs and that the block-and-bridge-preserving (BBP) subgraph isomorphism is a suitable matching operator in the  ...  SAR context, we propose a polynomial algorithm that computes a maximum common subgraph of two outerplanar graphs.  ...  Using this idea of the BBP subgraph isomorphism, we propose a polynomial MCS algorithm for outerplanar graphs.  ... 
doi:10.3233/aic-2010-0482 fatcat:kguu6ugombfx7bvfia64d6mqii

Designing Low-Congestion Networks with Structural Graph Theory

Yota OTACHI
2011 Interdisciplinary Information Sciences  
We apply some newest results in Graph Minor Theory to the problem, and obtain efficient (even best possible) algorithms.  ...  In these lecture notes, we study problems of designing low-congestion subnetworks of given networks.  ...  Using such an algorithm, design a lineartime algorithm for testing outerplanarity. Solution (Exercise 2.6).  ... 
doi:10.4036/iis.2011.197 fatcat:tzxj4vzsbvacndnb4mofpvrjz4

Computing Minimum Cycle Bases in Weighted Partial 2-Trees in Linear Time [article]

Carola Doerr, G. Ramakrishna, Jens M. Schmidt
2014 arXiv   pre-print
Such an improvement was achieved previously only for outerplanar graphs [Liu and Lu: Minimum Cycle Bases of Weighted Outerplanar Graphs, IPL 110:970--974, 2010].  ...  We present a linear time algorithm for computing an implicit linear space representation of a minimum cycle basis (MCB) in weighted partial 2-trees, i.e., graphs of treewidth two.  ...  Narayanaswamy for fruitful discussions during the early stages of this work.  ... 
arXiv:1303.0728v2 fatcat:lg4znhrg3rao7acfxlyilj2g74

Effective feature construction by maximum common subgraph sampling

Leander Schietgat, Fabrizio Costa, Jan Ramon, Luc De Raedt
2010 Machine Learning  
The maximum common subgraphs are computed under the block-and-bridge-preserving subgraph isomorphism from the outerplanar examples in polynomial time.  ...  We take a different approach: rather than mining for all optimal local patterns, we extract features from the set of pairwise maximum common subgraphs.  ...  For trees, which are special outerplanar graphs (they are block-free), the BBP subgraph isomorphism is equivalent to the subtree isomorphism.  ... 
doi:10.1007/s10994-010-5193-8 fatcat:hbcar6o3bjcrrddbf35qmk3ghe

Computing and Drawing Isomorphic Subgraphs [chapter]

Sabine Bachl, Franz-Josef Brandenburg
2002 Lecture Notes in Computer Science  
Then we present two different heuristics for the computation of maximal connected isomorphic subgraphs. Both heuristics use weighting functions and have been tested on four independent test suites.  ...  In this paper we show that the isomorphic subgraph problem is NP-hard, even for restricted instances such as connected outerplanar graphs.  ...  These graphs where chosen by the following reasoning. For each graph from the first test suite the optimal result has been computed by an exhaustive search algorithm.  ... 
doi:10.1007/3-540-36151-0_8 fatcat:saihqp3yqnaevm6qrbjnazxujm

Computing and Drawing Isomorphic Subgraphs [chapter]

S. Bachl, F. -J. Brandenburg, D. Gmach
2006 Graph Algorithms and Applications 5  
Then we present two different heuristics for the computation of maximal connected isomorphic subgraphs. Both heuristics use weighting functions and have been tested on four independent test suites.  ...  In this paper we show that the isomorphic subgraph problem is NP-hard, even for restricted instances such as connected outerplanar graphs.  ...  These graphs where chosen by the following reasoning. For each graph from the first test suite the optimal result has been computed by an exhaustive search algorithm.  ... 
doi:10.1142/9789812773289_0013 fatcat:7deekd4hqraafodsgtbpeuhywu

Computing and Drawing Isomorphic Subgraphs

Sabine Bachl, Franz J. Brandenburg, Daniel Gmach
2004 Journal of Graph Algorithms and Applications  
Then we present two different heuristics for the computation of maximal connected isomorphic subgraphs. Both heuristics use weighting functions and have been tested on four independent test suites.  ...  In this paper we show that the isomorphic subgraph problem is NP-hard, even for restricted instances such as connected outerplanar graphs.  ...  These graphs where chosen by the following reasoning. For each graph from the first test suite the optimal result has been computed by an exhaustive search algorithm.  ... 
doi:10.7155/jgaa.00090 fatcat:vlbqwuwzsbdkhktxhviz4fwgdm

Fast approximation schemes for K3, 3-minor-free or K5-minor-free graphs

Mohammadtaghi Hajiaghayi, Naomi Nishimura, Prabhakar Ragde, Dimitrios M. Thilikos
2001 Electronic Notes in Discrete Mathematics  
As a result, we can design practical polynomial-time approximation schemes for both minimization and maximization problems on these classes of non-planar graphs.  ...  As the class of graphs of bounded treewidth is of limited size, we n e e d t o s o l v e NP-hard problems for wider classes of graphs than this class.  ...  Thus the solutions converge toward optimal as n increases. u t We can generalize this approach for testing graph isomorphism of a xed pattern H: Theorem 16.  ... 
doi:10.1016/s1571-0653(04)00379-8 fatcat:ipvamhg3ovdmvapv3cypfkqyk4

The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

T. Calamoneri
2006 Computer journal  
The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs.  ...  This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach.  ...  Petreschi for their careful reading of the preliminary versions of this paper, and to all people who have contributed to improve the paper and to enrich the web page.  ... 
doi:10.1093/comjnl/bxl018 fatcat:3dmkmvdgbjhmflhslynszzh4h4
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