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

2014
*
arXiv
*
pre-print

We provide

arXiv:1403.5702v3
fatcat:kngk5qubmbh4paakqn7vy5lzdm
*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*. ...##
###
A polynomial-time algorithm for Outerplanar Diameter Improvement

2017
*
Journal of computer and system sciences (Print)
*

We provide

doi:10.1016/j.jcss.2017.05.016
fatcat:rpcq6iwxcnay5p6dtrimyvh76a
*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. ...##
###
A Polynomial-Time Algorithm for Outerplanar Diameter Improvement
[chapter]

2015
*
Lecture Notes in Computer Science
*

We provide

doi:10.1007/978-3-319-20297-6_9
fatcat:a4p5f5vlkvfk5n5bdvgeebifbe
*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. ...##
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Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner's Contraction

2007
*
Algorithmica
*

Second, we obtain explicit (and

doi:10.1007/s00453-007-9138-y
fatcat:4f2pu7hlyvdafbbucfgwcdysky
*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. ...##
###
Algorithmic aspects of distance constrained labeling: a survey

2014
*
International Journal of Networking and Computing
*

From the viewpoint of theory, the upper bounds on the labeling numbers and the

doi:10.15803/ijnc.4.2_251
fatcat:2u6f2vwnuzfwjom55mfsfhc6sa
*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] . ...##
###
Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner's Contraction
[chapter]

2006
*
Lecture Notes in Computer Science
*

Second, we obtain explicit (and

doi:10.1007/11940128_3
fatcat:wwmk2n26qjcqrim5vlmi255mde
*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. ...##
###
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

2006
*
Computer journal
*

This paper reviews the results from previous by published literature, looking at the problem with

doi:10.1093/comjnl/bxl018
fatcat:3dmkmvdgbjhmflhslynszzh4h4
*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. ...##
###
Disjoint paths in sparse graphs

2009
*
Discrete Applied Mathematics
*

Yannakakis, Primal-dual approximation

doi:10.1016/j.dam.2009.03.009
fatcat:sp573pvvnrgdrgb6flpxilanoe
*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. ...##
###
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

2011
*
Computer journal
*

This paper reviews the results from previous by published literature, looking at the problem with

doi:10.1093/comjnl/bxr037
fatcat:d767iuwpizajhcczsdat2inoki
*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*. ...##
###
Approximation algorithms for NP-complete problems on planar graphs

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. ...

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

2019
*
International Symposium on Parameterized and Exact Computation
*

Our techniques can also be used to show that the embedded k-

doi:10.4230/lipics.ipec.2018.25
dblp:conf/iwpec/LokshtanovO018
fatcat:sew3gycc6fb23ljuhgudiwpag4
*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. ...##
###
Approximation algorithms for NP-complete problems on planar graphs

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. ...

##
###
Augmenting Outerplanar Graphs to Meet Diameter Requirements

2013
*
Journal of Graph Theory
*

In this paper, we give the first constant factor approximation

doi:10.1002/jgt.21719
fatcat:nkebqmfbzvhvjcsaixrbpyz4ty
*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) . ...##
###
Approximations for -Colorings of Graphs

2004
*
Computer journal
*

We also give approximation

doi:10.1093/comjnl/47.2.193
fatcat:gfexzen2gbcgzhm65paojzqtq4
*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. ...
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