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Approximating the treewidth of AT-free graphs

Vincent Bouchitté, Ioan Todinca
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
Using the speciÿc structure of the minimal separators of AT-free graphs, we give a polynomial time algorithm that computes a triangulation whose width is no more than twice the treewidth of the input graph  ...  Using the particular structure of their minimal separators, we give a 2-approximation algorithm for the treewidth of AT-free graphs.  ...  By dichotomy, the 2-approximation algorithm for the treewidth of AT-free graphs works in O(n 5:5 log n). We prove ÿrst the correctness of our algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-218x(02)00414-6">doi:10.1016/s0166-218x(02)00414-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6d5hvhzqpvh3djn23sayghpxau">fatcat:6d5hvhzqpvh3djn23sayghpxau</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170928194655/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/6c2/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDE2NjIxOHgwMjAwNDE0Ng%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9b/96/9b963ab52e64c44f1e494496e351cda46d205f6e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0166-218x(02)00414-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Approximating the Treewidth of AT-Free Graphs [chapter]

Vincent Bouchitté, Ioan Todinca
<span title="">2000</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Using the speciÿc structure of the minimal separators of AT-free graphs, we give a polynomial time algorithm that computes a triangulation whose width is no more than twice the treewidth of the input graph  ...  Using the particular structure of their minimal separators, we give a 2-approximation algorithm for the treewidth of AT-free graphs.  ...  By dichotomy, the 2-approximation algorithm for the treewidth of AT-free graphs works in O(n 5:5 log n). We prove ÿrst the correctness of our algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-40064-8_7">doi:10.1007/3-540-40064-8_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4plabhbix5bibeemuyzl7woxrq">fatcat:4plabhbix5bibeemuyzl7woxrq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170928194655/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/6c2/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDE2NjIxOHgwMjAwNDE0Ng%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9b/96/9b963ab52e64c44f1e494496e351cda46d205f6e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-40064-8_7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Linearity of grid minors in treewidth with applications through bidimensionality

Erik D. Demaine, Mohammadtaghi Hajiaghayi
<span title="">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ujm6quky2va7pmzbitmgsrksbu" style="color: black;">Combinatorica</a> </i> &nbsp;
We prove that any H-minor-free graph, for a fixed graph H, of treewidth w has an Ω(w) × Ω(w) grid graph as a minor.  ...  The approach of this paper can be viewed more generally as a framework for extending combinatorial results on planar graphs to hold on H-minor-free graphs for any fixed H.  ...  Seymour for many helpful discussions and for providing a portal into the Graph Minor Theory and revealing some of its hidden structure that we use in this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00493-008-2140-4">doi:10.1007/s00493-008-2140-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cff2tl55u5bubhmz65rewhxpoa">fatcat:cff2tl55u5bubhmz65rewhxpoa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100613123006/http://erikdemaine.org/papers/GridMinors_Combinatorica/paper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/84/40/844010458bda1bc7f5f625ec4625eb27ff79feb2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00493-008-2140-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Approximation algorithms for classes of graphs excluding single-crossing graphs as minors

Erik D Demaine, MohammadTaghi Hajiaghayi, Naomi Nishimura, Prabhakar Ragde, Dimitrios M Thilikos
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
The classes considered are those formed by excluding as a minor a graph that can be embedded in the plane with at most one crossing.  ...  Finally, we make use of the structural properties to derive polynomial-time algorithms for approximating treewidth within a factor of 1.5 and branchwidth within a factor of 2.25 as well as polynomial-time  ...  A famous open problem is whether treewidth can be approximated within a constant factor. Constant-factor approximations are possible on AT-free graphs [BT01, BKMT01] and on planar graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2003.12.001">doi:10.1016/j.jcss.2003.12.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zg6epgwkerenrodjedvj3pzbyy">fatcat:zg6epgwkerenrodjedvj3pzbyy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171001190619/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/a8d/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDAyMjAwMDAwNDAwMDE5NA%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3a/f3/3af3caf44726aaf83fc33b9827cb36aa2ce4e976.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2003.12.001"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

The Bidimensionality Theory and Its Algorithmic Applications

E. D. Demaine, M. Hajiaghayi
<span title="2007-11-23">2007</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bf4qaipmsrghrjyxonrsmqevie" style="color: black;">Computer journal</a> </i> &nbsp;
This theory characterizes a broad range of graph problems ("bidimensional") that admit efficient approximate or fixed-parameter solutions in a broad range of graphs.  ...  This paper surveys the theory of bidimensionality.  ...  a graph of treewidth at most c H k.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/comjnl/bxm033">doi:10.1093/comjnl/bxm033</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kqdeonxjbbh4vg3e5nuw62ym7u">fatcat:kqdeonxjbbh4vg3e5nuw62ym7u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070824192435/http://erikdemaine.org/papers/BidimensionalSurvey_CJ/paper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/13/a413d06cc07cf3f0672acc63896b88db7e7caa9e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/comjnl/bxm033"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Fast Algorithms for Hard Graph Problems: Bidimensionality, Minors, and Local Treewidth [chapter]

Erik D. Demaine, MohammadTaghi Hajiaghayi
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This paper surveys the theory of bidimensional graph problems.  ...  We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems.  ...  To achieve this level of generality, [DH05a] uses the sublinear parameter-treewidth bound of Theorem 5 as well as a recent O(1)-approximation algorithm for treewidth in H-minor-free graphs [FHL04] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31843-9_57">doi:10.1007/978-3-540-31843-9_57</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bl5d75gm7nechmehbwv2blc33m">fatcat:bl5d75gm7nechmehbwv2blc33m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829222438/http://www-math.mit.edu/~hajiagha/GD04.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7e/dc/7edc61e421b017c4230c73ce5c50fc37450e64ba.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31843-9_57"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Fast partitioning l-apex graphs with applications to approximating maximum induced-subgraph problems

Dimitrios M. Thilikos, Hans L. Bodlaender
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5xfy4fcdxvcvdiybp6iqbffqc4" style="color: black;">Information Processing Letters</a> </i> &nbsp;
In this paper we show that the vertex set of any graph not containing an lapex graph as a minor can be quickly partitioned into 2 l sets inducing graphs with small treewidth.  ...  A graph is l-apex if it can be made planar by removing at most l vertices.  ...  Given a planar graph H, w e de ne the minimum excluding bound of H, medH, as the maximum treewidth over all H-minor free graphs. as the minimum k bounding the treewidth of H-minor free graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0020-0190(97)00024-0">doi:10.1016/s0020-0190(97)00024-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hddilfcyszduvmoqp5udlfb7q4">fatcat:hddilfcyszduvmoqp5udlfb7q4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20080425160721/http://www.cs.uu.nl/research/techreps/repo/CS-1996/1996-30.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ce/7d/ce7d81cb0aaf0d394fa23460fbc0cfb996ff684b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0020-0190(97)00024-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Approximate MAP Estimation for Pairwise Potentials via Baker's Technique [article]

Yi-Kai Wang
<span title="2018-04-17">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that computing MAX 2-CSP admits polynomial-time approximation scheme (PTAS) on planar graphs, graphs with bounded local treewidth, H-minor-free graphs, geometric graphs with bounded density and  ...  We propose a unified framework to model these computation tasks where the structures of these optimization problems are encoded by functions attached on the vertices and edges of a graph.  ...  + 1 sets such that any k of the sets induce a graph of treewidth at most c H k.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1412.0340v4">arXiv:1412.0340v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bwu3jpcq3fc5bgpugzpvmfwnri">fatcat:bwu3jpcq3fc5bgpugzpvmfwnri</a> </span>
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Algorithmic Graph Minor Theory: Improved Grid Minor Bounds and Wagner's Contraction

Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ichi Kawarabayashi
<span title="2007-12-14">2007</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qhi3z76be5c5xeihac5cyiid3m" style="color: black;">Algorithmica</a> </i> &nbsp;
We explore the three main avenues of research still unsolved in the algorithmic graph-minor theory literature, which all stem from a key min-max relation between the treewidth of a graph and its largest  ...  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  ...  , every K 3,k -minor-free graph of treewidth at least c k r has an r×r grid minor.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-007-9138-y">doi:10.1007/s00453-007-9138-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4f2pu7hlyvdafbbucfgwcdysky">fatcat:4f2pu7hlyvdafbbucfgwcdysky</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706082526/http://www-math.mit.edu/%7Ehajiagha/wagnercontraction.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c9/b6/c9b61aca642f38e7fc24c615c5605831a15c876b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00453-007-9138-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

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

Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ichi Kawarabayashi
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We explore the three main avenues of research still unsolved in the algorithmic graph-minor theory literature, which all stem from a key min-max relation between the treewidth of a graph and its largest  ...  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  ...  , every K 3,k -minor-free graph of treewidth at least c k r has an r×r grid minor.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11940128_3">doi:10.1007/11940128_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wwmk2n26qjcqrim5vlmi255mde">fatcat:wwmk2n26qjcqrim5vlmi255mde</a> </span>
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Approximation Algorithms via Structural Results for Apex-Minor-Free Graphs [chapter]

Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ichi Kawarabayashi
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
generalize the notion of vortices to "quasivortices" of bounded treewidth, proving a conjecture from [10].  ...  The second approximation result is a PTAS for unweighted TSP in apexminor-free graphs, which generalizes PTASs for TSP in planar graphs and bounded-genus graphs [20, 2, 24, 15] .  ...  We thank Paul Seymour for helpful suggestions and intuition about the structure of apex-minor-free graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02927-1_27">doi:10.1007/978-3-642-02927-1_27</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/en2uxhqyxraznbrc4cyucem64e">fatcat:en2uxhqyxraznbrc4cyucem64e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170815140327/https://core.ac.uk/download/pdf/21174058.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c3/b9/c3b9e50b9f0e5453df7eefb6ed87034b0a6a94de.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02927-1_27"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Approximation Schemes for Planar Graph Problems [chapter]

Erik D. Demaine, MohammadTaghi Hajiaghayi
<span title="">2008</span> <i title="Springer US"> Encyclopedia of Algorithms </i> &nbsp;
The first step in this approach is to find a separator of O( √ n) vertices or edges, where n is the size of the graph, whose removal splits the graph into two or more pieces each of which is a constant  ...  of (1 + )-approximation algorithms for all > 0.  ...  Eppstein [10] generalized Baker's approach to a broader class of graphs called graphs of bounded local treewidth, i.e., where the treewidth of the subgraph induced by the set of vertices at distance  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-0-387-30162-4_32">doi:10.1007/978-0-387-30162-4_32</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kad2i2t5gres3oua25e3xklc3u">fatcat:kad2i2t5gres3oua25e3xklc3u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090116012812/http://erikdemaine.org/papers/PlanarApprox_Encyclopedia2008/paper.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/38/70/3870522f3891b9351c215b15183710b82bb25386.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-0-387-30162-4_32"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

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

Mohammadtaghi Hajiaghayi, Naomi Nishimura, Prabhakar Ragde, Dimitrios M. Thilikos
<span title="">2001</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fhi2xwpnh5gmlgof2idwu5wlgq" style="color: black;">Electronic Notes in Discrete Mathematics</a> </i> &nbsp;
A graph G has locally bounded t r eewidth if for each v ertex v of G, the treewidth of the subgraph of G induced on all vertices of distance at most r from v is only a function of r, called local treewidth  ...  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.  ...  o n tains K 3 3 -minor-free graphs and K 5 -minor-free graphs, and showed the graphs in the class have linear local treewidth.  ... 
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Time and Parallelizability Results for Parity Games with Bounded Treewidth [chapter]

John Fearnley, Sven Schewe
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
, and number of priorities in the parity game.  ...  Consequently, researchers have considered specialised algorithms for the case where certain graph parameters are small.  ...  For example, it has been shown that the control flow graphs of goto free Pascal programs have treewidth at most 3, and that the control flow graphs of goto free C programs have treewidth at most 6 [13  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-31585-5_20">doi:10.1007/978-3-642-31585-5_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s222lmrcubb3fhgexdch7nv57a">fatcat:s222lmrcubb3fhgexdch7nv57a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190226075732/http://pdfs.semanticscholar.org/6e6b/a49ed5d56af69a6a50363d6bc24c4e51983a.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6e/6b/6e6ba49ed5d56af69a6a50363d6bc24c4e51983a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-31585-5_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Low Treewidth Embeddings of Planar and Minor-Free Metrics [article]

Arnold Filtser, Hung Le
<span title="2022-03-29">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Cohen-Addad, Filtser, Klein and Le [FOCS'20] constructed a stochastic embedding of minor-free graphs of diameter D into graphs of treewidth O_ϵ(log n) with expected additive distortion +ϵ D.  ...  We also significantly improve the running time of the QPTAS for the metric Baker's problems in minor-free graphs from n^O_ϵ(log(n)) to n^O_ϵ(loglog(n))^3.  ...  Acknowledgments The authors are grateful to Philip Klein and Vincent Cohen-Addad for helpful conversations.  ... 
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