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Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs

Philip N. Klein, Claire Mathieu, Hang Zhou, Marc Herbstritt
2015 Symposium on Theoretical Aspects of Computer Science  
For planar graphs, we prove that correlation clustering reduces to two-edge-connected augmentation, and that both problems have a polynomial-time approximation scheme.  ...  In two-edge-connected augmentation, the input is a graph with edge-weights and a subset R of edges of the graph.  ...  Karloff for helping make the connection between correlation clustering and two-edge-connected augmentation in planar graphs; Nabil Mustafa for numerous discussions; and Grigory Yaroslavtsev.  ... 
doi:10.4230/lipics.stacs.2015.554 dblp:conf/stacs/KleinMZ15 fatcat:7h7w2543qbdbxixjf25ijziacq

Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs [chapter]

Marc Lelarge, Hang Zhou
2013 Lecture Notes in Computer Science  
Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs. Philip Klein, Claire Mathieu, and Hang Zhou.  ...  , Switzerland, 2016 Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs -STACS conference, Germany, 2015 -Dagstuhl seminar, Germany, 2016  ... 
doi:10.1007/978-3-642-45030-3_14 fatcat:cs27muh23fgejlpec7j3pdqmie

Algorithms for Optimization Problems in Planar Graphs (Dagstuhl Seminar 16221)

Jeff Erickson, Philip N. Klein, Dániel Marx, Claire Mathieu, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 16221 "Algorithms for Optimization Problems in Planar Graphs". The seminar was held from May 29 to June 3, 2016.  ...  This report contains abstracts for the recent developments in planar graph algorithms discussed during the seminar as well as summaries of open problems in this area of research.  ...  Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs Hang Zhou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.4230/dagrep.6.5.94 dblp:journals/dagstuhl-reports/EricksonKMM16 fatcat:wasdfgivt5fqdppfxo3iqqs2ta

Narrowing the LOCALx2013CONGEST Gaps in Sparse Networks via Expander Decompositions [article]

Yi-Jun Chang, Hsin-Hao Su
2022 arXiv   pre-print
independent set, and correlation clustering, in graphs excluding a fixed minor in the CONGEST model.  ...  This class of graphs covers many sparse network classes that have been studied in the literature, including planar graphs, bounded-genus graphs, and bounded-treewidth graphs.  ...  Correlation Clustering In the agreement maximization correlation clustering problem, the edge set is partitioned into E = E + ∪E − two parts, and the goal is to compute a clustering of the vertices V =  ... 
arXiv:2205.08093v1 fatcat:h2wxmhc3lnhtdcghxhogjqbgre

Hierarchical Planar Correlation Clustering for Cell Segmentation [chapter]

Julian Yarkony, Chong Zhang, Charless C. Fowlkes
2015 Lecture Notes in Computer Science  
We introduce a novel algorithm for hierarchical clustering on planar graphs we call "Hierarchical Greedy Planar Correlation Clustering" (HGPCC).  ...  Planar correlation clustering is NP hard but the efficient Pla-narCC solver allows for efficient and accurate approximate inference. We demonstrate HGPCC on problems in segmenting images of cells.  ...  Our method exploits the fact that correlation clustering can often be done efficiently on planar graphs with very high degrees of accuracy.  ... 
doi:10.1007/978-3-319-14612-6_36 fatcat:y6sv2qwtanabhpffitbtyr7wwy

Fast Planar Correlation Clustering for Image Segmentation [chapter]

Julian Yarkony, Alexander Ihler, Charless C. Fowlkes
2012 Lecture Notes in Computer Science  
We describe a new optimization scheme for finding highquality clusterings in planar graphs that uses weighted perfect matching as a subroutine.  ...  Our method provides lower-bounds on the energy of the optimal correlation clustering that are typically fast to compute and tight in practice.  ...  It then searches for inconsistent edges, namely cut edges that connect two nodes that lie within the same connected component.  ... 
doi:10.1007/978-3-642-33783-3_41 fatcat:nx24rlaybzcthjzfhmcuk6twzy

Fast Planar Correlation Clustering for Image Segmentation [article]

Julian Yarkony, Alexander T. Ihler, Charless C. Fowlkes
2012 arXiv   pre-print
We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine.  ...  Our method provides lower-bounds on the energy of the optimal correlation clustering that are typically fast to compute and tight in practice.  ...  It then searches for inconsistent edges, namely cut edges that connect two nodes that lie within the same connected component.  ... 
arXiv:1208.0378v1 fatcat:pvcexygznfh53frurjl23eqciu

A PTAS for subset TSP in minor-free graphs [article]

Hung Le
2019 arXiv   pre-print
The main technical ingredient in our PTAS is a construction of a nearly light subset (1+ϵ)-spanner for any given edge-weighted H-minor-free graph.  ...  This improves the earlier lightness bound ϵ^-O(d) obtained by Borradaile, Le and Wulff-Nilsen. _ An (1+ϵ)-spanner with sublinear lightness for any metric of constant correlation dimension.  ...  CCF-1252833, a NSERC grant and a PIMS postdoctoral fellowship.  ... 
arXiv:1804.01588v3 fatcat:tdrgbwz54rev5gl55t7lxrgxqm

Narrowing the LOCAL-CONGEST Gaps in Sparse Networks via Expander Decompositions

Yi-Jun Chang, Hsin-Hao Su
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018].  ...  Many combinatorial optimization problems, including maximum weighted matching and maximum independent set, can be approximated within (1±𝜖) factors in poly(log 𝑛, 1/𝜖) rounds in the LOCAL model via  ...  Correlation Clustering In the agreement maximization correlation clustering problem, the edge set is partitioned into 𝐸 = 𝐸 + ∪ 𝐸 − two parts, and the goal is to compute a clustering of the vertices  ... 
doi:10.1145/3519270.3538423 fatcat:jv7pwb6wmrhjfirawnl2v4qdra

Graph Theory Based Approach to Characterize Self Interstitial Defect Morphology [article]

Utkarsh Bhardwaj, Andrea E. Sand, Manoj Warrier
2020 arXiv   pre-print
We present a method to characterize a defect's morphology precisely by reducing the problem into graph theoretical concepts of finding connected components and cycles.  ...  We highlight our method's comparative advantage for its completeness, computational speed, and quantitative details.  ...  Whether to join two nodes in the graph with an edge is predicated upon rules defined separately for parallel and non-parallel ring-like configurations.  ... 
arXiv:2009.14147v2 fatcat:ncyuh66cmzhpzplyzjxk32wgia

A survey of parameterized algorithms and the complexity of edge modification [article]

Christophe Crespelle, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach
2020 arXiv   pre-print
The survey provides an overview of the developing area of parameterized algorithms for graph modification problems.  ...  We concentrate on edge modification problems, where the task is to change a small number of adjacencies in a graph in order to satisfy some required property.  ...  We thank Marcin Pilipczuk, William Lochet, and Dekel Tsur for helpful comments. References  ... 
arXiv:2001.06867v2 fatcat:6ogysat6n5drpbxsvs63zjmega

On the double random current nesting field [article]

Hugo Duminil-Copin, Marcin Lis
2019 arXiv   pre-print
More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph  ...  We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model.  ...  Acknowledgments M.L. is grateful to Sanjay Ramassamy for an inspiring remark, and the authors thank Aran Raoufi and Gourab Ray for many useful discussions.  ... 
arXiv:1712.02305v2 fatcat:kj56amp6nvg4zbxrli7oplgkpy

On the double random current nesting field

Hugo Duminil-Copin, Marcin Lis
2019 Probability theory and related fields  
More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph  ...  We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model.  ...  For a current ω, a connected component of the graph (V , ω) will be called a cluster.  ... 
doi:10.1007/s00440-019-00899-0 fatcat:gpvxvs4i2naofnohv2fnxi3eey

Visual Exploration of Complex Time-Varying Graphs

Gautam Kumar, Michael Garland
2006 IEEE Transactions on Visualization and Computer Graphics  
However, they often produce extremely tangled results and exhibit impractical running times for highly non-planar graphs with large edge density.  ...  Rather than displaying all edges and nodes at once, resulting in a convoluted rendering, we present an interactive tool that filters edges and nodes using the graph hierarchy and allows users to drill  ...  We construct a graph where two stocks are connected by an edge when their returns correlations are above a selected threshold. Such graphs are known to have power law degree distributions [3] .  ... 
doi:10.1109/tvcg.2006.193 pmid:17080803 fatcat:izhtmziuh5hrfbzkkor4w5olvm

Visualization Model for Monitoring of Computer Networks Security Based on the Analogue of Voronoi Diagrams [chapter]

Maxim Kolomeets, Andrey Chechulin, Igor Kotenko
2016 Lecture Notes in Computer Science  
This research is being supported by the Ministry of Education and Science of The Russian Federation (contract 14.604.21.0137, unique contract identifier RFMEFI60414X0137) in SPIIRAS.  ...  Discussion Based Graphs are not restricted in display of size and color of vertices, size and color of connections, clustering, and can also display any topological types.  ...  Graphs also can display hosts and connections by a limited set of geometric shapes to be visualized in 3D, provided that clustering of the vertices is done.  ... 
doi:10.1007/978-3-319-45507-5_10 fatcat:hquqhvkilvc3likooawpdivatq
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