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A Polynomial-time Algorithm for Outerplanar Diameter Improvement [article]

Nathann Cohen, Daniel Gonçalves, Eun Jung Kim, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos, Mathias Weller
2014 arXiv   pre-print
We provide a dynamic programming algorithm that solves this problem in polynomial time.  ...  The Outerplanar Diameter Improvement problem asks, given a graph G and an integer D, whether it is possible to add edges to G in a way that the resulting graph is outerplanar and has diameter at most D  ...  2 solves Outerplanar Diameter Improvement for disconnected input graphs in polynomial time.  ... 
arXiv:1403.5702v3 fatcat:kngk5qubmbh4paakqn7vy5lzdm

A polynomial-time algorithm for Outerplanar Diameter Improvement

Nathann Cohen, Daniel Gonçalves, Eun Jung Kim, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos, Mathias Weller
2017 Journal of computer and system sciences (Print)  
We provide a dynamic programming algorithm that solves this problem in polynomial time.  ...  The Outerplanar Diameter Improvement problem asks, given a graph G and an integer D, whether it is possible to add edges to G in a way that the resulting graph is outerplanar and has diameter at most D  ...  In this work, we show that Outerplanar Diameter Improvement is polynomial-time solvable.  ... 
doi:10.1016/j.jcss.2017.05.016 fatcat:rpcq6iwxcnay5p6dtrimyvh76a

A Polynomial-Time Algorithm for Outerplanar Diameter Improvement [chapter]

Nathann Cohen, Daniel Gonçalves, Eunjung Kim, Christophe Paul, Ignasi Sau, Dimitrios M. Thilikos, Mathias Weller
2015 Lecture Notes in Computer Science  
We provide a dynamic programming algorithm that solves this problem in polynomial time.  ...  The Outerplanar Diameter Improvement problem asks, given a graph G and an integer D, whether it is possible to add edges to G in a way that the resulting graph is outerplanar and has diameter at most D  ...  In this work, we show that Outerplanar Diameter Improvement is polynomial-time solvable.  ... 
doi:10.1007/978-3-319-20297-6_9 fatcat:a4p5f5vlkvfk5n5bdvgeebifbe

Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner's Contraction

Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ichi Kawarabayashi
2007 Algorithmica  
Second, we obtain explicit (and improved) bounds on the min-max relation for an important class of graphs excluding a minor, namely, K 3,k -minor-free graphs, using new techniques that do not rely on Graph  ...  This result demonstrates the limitations of a general theory of algorithms for the family of contraction-closed problems (which includes, for example, the celebrated dominating-set problem).  ...  Acknowledgments We thank László Lovász and Robin Thomas for helpful discussions.  ... 
doi:10.1007/s00453-007-9138-y fatcat:4f2pu7hlyvdafbbucfgwcdysky

Algorithmic aspects of distance constrained labeling: a survey

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno
2014 International Journal of Networking and Computing  
From the viewpoint of theory, the upper bounds on the labeling numbers and the time complexity of finding a minimum labeling are intensively and extensively studied.  ...  In this paper, we survey the distance constrained labeling problems from algorithmic aspects, that is, computational complexity, approximability, exact computation, and so on.  ...  For outerplanar graphs, a polynomial-time algorithm is known, though the degree of the polynomial is large [48] .  ... 
doi:10.15803/ijnc.4.2_251 fatcat:2u6f2vwnuzfwjom55mfsfhc6sa

Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner's Contraction [chapter]

Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ichi Kawarabayashi
2006 Lecture Notes in Computer Science  
Second, we obtain explicit (and improved) bounds on the min-max relation for an important class of graphs excluding a minor, namely, K 3,k -minor-free graphs, using new techniques that do not rely on Graph  ...  This result demonstrates the limitations of a general theory of algorithms for the family of contraction-closed problems (which includes, for example, the celebrated dominating-set problem).  ...  Acknowledgments We thank László Lovász and Robin Thomas for helpful discussions.  ... 
doi:10.1007/11940128_3 fatcat:wwmk2n26qjcqrim5vlmi255mde

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

T. Calamoneri
2006 Computer journal  
This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach.  ...  differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k.  ...  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

Disjoint paths in sparse graphs

Cédric Bentz
2009 Discrete Applied Mathematics  
Yannakakis, Primal-dual approximation algorithms for integral flow and multicut in trees, Algorithmica 18 (1997) 3-20] to graphs with a fixed cyclomatic number, while this cannot be achieved for other  ...  We also introduce the k-edge-outerplanar graphs, a class of planar graphs with arbitrary (but bounded) tree-width that generalizes the cacti, and show that the integrality gap of the maximum edge-disjoint  ...  Acknowledgments The author thanks the anonymous referees for their useful comments and remarks.  ... 
doi:10.1016/j.dam.2009.03.009 fatcat:sp573pvvnrgdrgb6flpxilanoe

Page 7693 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
We present polynomial time algorithms for solving the p-facility k-centrum problem on path and tree graphs. These algorithms can be combined with the general approximation al- gorithms of Y.  ...  We prove that this number agrees with a polynomial in A for any sufficiently large A, and we establish a generalization of Whitney’s broken circuit theorem by applying a recent improvement of the inclusion  ... 

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

T. Calamoneri
2011 Computer journal  
This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author.  ...  differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k.  ...  Figure 8 : 8 A counterexample outerplanar graph with ∆ = 4 and λ 2,1 = ∆ + 3. 1 2 1 − , for any > 0, unless NP-problems have randomized polynomial time algorithms.  ... 
doi:10.1093/comjnl/bxr037 fatcat:d767iuwpizajhcczsdat2inoki

Approximation algorithms for NP-complete problems on planar graphs

Brenda S. Baker
1994 Journal of the ACM  
For these and certain other problems, the proof of solvability on k-outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time.  ...  For general planar graphs, if the problem is a maximization problem, such as maximum independent set, this technique gives for each k a linear time algorithm that produces a solution whose size is at least  ...  A Linear-Time Algorithm for OuterPlanar Graphs In this section, we show how to solve the maximum independent set problem in linear time for outerplanar graphs.  ... 
doi:10.1145/174644.174650 fatcat:sqam42w5mnhsvhho2mslrq7nfi

A Strongly-Uniform Slicewise Polynomial-Time Algorithm for the Embedded Planar Diameter Improvement Problem

Daniel Lokshtanov, Mateus De Oliveira Oliveira, Saket Saurabh, Michael Wagner
2019 International Symposium on Parameterized and Exact Computation  
Our techniques can also be used to show that the embedded k-outerplanar diameter improvement problem (k-EOPDI), a variant of EPDI where the resulting graph is required to be k-outerplanar instead of planar  ...  In the embedded planar diameter improvement problem (EPDI) we are given a graph G embedded in the plane and a positive integer d.  ...  The algorithm for solving the embedded k-outerplanar diameter improvement problem is almost identical to the one to solve the embedded planar diameter improvement problem.  ... 
doi:10.4230/lipics.ipec.2018.25 dblp:conf/iwpec/LokshtanovO018 fatcat:sew3gycc6fb23ljuhgudiwpag4

Approximation algorithms for NP-complete problems on planar graphs

Brenda S. Baker
1983 24th Annual Symposium on Foundations of Computer Science (sfcs 1983)  
For these and certain other problems, the proof of solvability on k-outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time.  ...  For general planar graphs, if the problem is a maximization problem, such as maximum independent set, this technique gives for each k a linear time algorithm that produces a solution whose size is at least  ...  A Linear-Time Algorithm for OuterPlanar Graphs In this section, we show how to solve the maximum independent set problem in linear time for outerplanar graphs.  ... 
doi:10.1109/sfcs.1983.7 dblp:conf/focs/Baker83 fatcat:j7e3fg222vcp7cjwailauwavqe

Augmenting Outerplanar Graphs to Meet Diameter Requirements

Toshimasa Ishii
2013 Journal of Graph Theory  
In this paper, we give the first constant factor approximation algorithm to the problem with an outerplanar graph G.  ...  We also show that if the target diameter D is even, then the case where G is a partial 2-tree is also approximable within a constant.  ...  The latter one has been improved to a (2 + 1/δ, δ 5 )-approximation algorithm for any integer δ > 0 due to Chepoi et al. (2006) .  ... 
doi:10.1002/jgt.21719 fatcat:nkebqmfbzvhvjcsaixrbpyz4ty

Approximations for -Colorings of Graphs

H. L. Bodlaender
2004 Computer journal  
We also give approximation algorithms for λ-coloring and compute upper bounds on the best possible λ for outerplanar graphs, graphs of treewidth k, permutation and split graphs.  ...  For split graphs, we give a bound of 1 2 1.5 + 2 and we show that there are split graphs G with λ(G) = ( 1.5 ). Similar results are also given for variations of the λ-coloring problem.  ...  Acknowledgements We thank Hans Zantema for useful discussions and the referees for valuable suggestions, including a sharpened bound for Theorem 8.  ... 
doi:10.1093/comjnl/47.2.193 fatcat:gfexzen2gbcgzhm65paojzqtq4
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