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Fast detection and display of symmetry in outerplanar graphs

1992
*
Discrete Applied Mathematics
*

These results are then expanded to obtain

doi:10.1016/0166-218x(92)90112-n
fatcat:gpzavtpif5hi7nzh362q6dvu7q
*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*. ...##
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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. ...

##
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Approximating the minimum hub cover problem on planar graphs

2015
*
Optimization Letters
*

Our

doi:10.1007/s11590-015-0876-5
fatcat:xzmopsaflrgjtdsl7nnridg2my
*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 . ...##
###
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

2018
*
Discrete Optimization
*

However, the run time

doi:10.1016/j.disopt.2017.12.002
fatcat:wtihkskgpzcabhylljn5rgxju4
*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 ...##
###
Hammock-on-ears decomposition: A technique for the efficient parallel solution of shortest paths and other problems
[chapter]

1994
*
Lecture Notes in Computer Science
*

We i m p r o ve previous bounds

doi:10.1007/3-540-58338-6_93
fatcat:jvnczhs265ditkcurk666tlddy
*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). ...##
###
Graph-based data mining for biological applications

2011
*
AI Communications
*

Motivated by the fact that the majority

doi:10.3233/aic-2010-0482
fatcat:kguu6ugombfx7bvfia64d6mqii
*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*. ...##
###
Designing Low-Congestion Networks with Structural Graph Theory

2011
*
Interdisciplinary Information Sciences
*

We apply some newest results in

doi:10.4036/iis.2011.197
fatcat:tzxj4vzsbvacndnb4mofpvrjz4
*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). ...##
###
Computing Minimum Cycle Bases in Weighted Partial 2-Trees in Linear Time
[article]

2014
*
arXiv
*
pre-print

Such an improvement was achieved previously only

arXiv:1303.0728v2
fatcat:lg4znhrg3rao7acfxlyilj2g74
*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. ...##
###
Effective feature construction by maximum common subgraph sampling

2010
*
Machine Learning
*

The maximum common subgraphs are computed under the block-

doi:10.1007/s10994-010-5193-8
fatcat:hbcar6o3bjcrrddbf35qmk3ghe
*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*. ...##
###
Computing and Drawing Isomorphic Subgraphs
[chapter]

2002
*
Lecture Notes in Computer Science
*

Then we present two different heuristics

doi:10.1007/3-540-36151-0_8
fatcat:saihqp3yqnaevm6qrbjnazxujm
*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*. ...##
###
Computing and Drawing Isomorphic Subgraphs
[chapter]

2006
*
Graph Algorithms and Applications 5
*

Then we present two different heuristics

doi:10.1142/9789812773289_0013
fatcat:7deekd4hqraafodsgtbpeuhywu
*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*. ...##
###
Computing and Drawing Isomorphic Subgraphs

2004
*
Journal of Graph Algorithms and Applications
*

Then we present two different heuristics

doi:10.7155/jgaa.00090
fatcat:vlbqwuwzsbdkhktxhviz4fwgdm
*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*. ...##
###
Fast approximation schemes for K3, 3-minor-free or K5-minor-free graphs

2001
*
Electronic Notes in Discrete Mathematics
*

As a result, we can design practical polynomial-time approximation schemes

doi:10.1016/s1571-0653(04)00379-8
fatcat:ipvamhg3ovdmvapv3cypfkqyk4
*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. ...##
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The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

2006
*
Computer journal
*

The L(h, k)-labelling problem has been intensively studied following many approaches

doi:10.1093/comjnl/bxl018
fatcat:3dmkmvdgbjhmflhslynszzh4h4
*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. ...
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