Access the full text.
Sign up today, get DeepDyve free for 14 days.
G. Kortsarz, Robert Krauthgamer, James Lee (2002)
Hardness of Approximation for Vertex-Connectivity Network Design Problems
Amir Alush, J. Goldberger (2012)
Ensemble Segmentation Using Efficient Integer Linear ProgrammingIEEE Transactions on Pattern Analysis and Machine Intelligence, 34
In our work: correlation clustering, 2-edge-connected augmentation. Open problem: Steiner version of the 2-edge-connected subgraph problem
F. Dorn, Eelko Penninkx, H. Bodlaender, F. Fomin (2010)
Efficient Exact Algorithms on Planar Graphs: Exploiting Sphere Cut DecompositionsAlgorithmica, 58
Connectivity problems (2005-2011): TSP, Steiner, 2-edge-connected subgraph, etc
A. Ben-Dor, R. Shamir, Z. Yakhini (1999)
Clustering gene expression patternsJournal of computational biology : a journal of computational molecular cell biology, 6 3-4
Björn Andres, Jörg Kappes, T. Beier, U. Köthe, F. Hamprecht (2011)
Probabilistic image segmentation with closedness constraints2011 International Conference on Computer Vision
S. Khuller, R. Thurimella (1992)
Approximation Algorithms for Graph AugmentationJ. Algorithms, 14
A. Gionis, H. Mannila, Taneli Mielikäinen, Panayiotis Tsaparas (2007)
Assessing data mining results via swap randomizationACM Trans. Knowl. Discov. Data, 1
Y. Bachrach, Pushmeet Kohli, V. Kolmogorov, Morteza Zadimoghaddam (2013)
Optimal Coalition Structure Generation in Cooperative Graph GamesProceedings of the AAAI Conference on Artificial Intelligence
Case 1: There is a path in H i between an internal vertex of P i + 1 (let v be this vertex) and South [ s k i , x i ] ∪ P i
P. Klein, S. Mozes (2011)
Multiple-Source Single-Sink Maximum Flow in Directed Planar Graphs in O(diameter · n log n) Time
S. Provan, R. Burk (1999)
Two-Connected Augmentation Problems in Planar GraphsJ. Algorithms, 32
A. Berger, M. Grigni (2007)
Minimum Weight 2-Edge-Connected Spanning Subgraphs in Planar Graphs
Case 1.1: There is a path in H i between v and South
A] and update I by I−{I ab } ab∈E
Moses Charikar, Venkatesan Guruswami, Anthony Wirth (2005)
Clustering with qualitative informationJ. Comput. Syst. Sci., 71
P. Klein, Brown UniversityAbstractWe (1992)
When cycles collapse: A general approximation technique for constrained two-connectivity problems
R. Jothi, B. Raghavachari, S. Varadarajan (2003)
A 5/4-approximation algorithm for minimum 2-edge-connectivity
N. Ailon, M. Charikar, Alantha Newman (2005)
Aggregating inconsistent information: ranking and clustering
F. Harary (1969)
Graph theory
DR Martin, CC Fowlkes, J Malik (2004)
Learning to detect natural image boundaries using local brightness, color, and texture cuesPattern Anal. Mach. Intell., 26
A Ben-Dor, R Shamir, Z Yakhini (1999)
Clustering gene expression patternsJ. Comput. Biol., 6
Sungwoong Kim, Sebastian Nowozin, Pushmeet Kohli, C. Yoo (2011)
Higher-Order Correlation Clustering for Image Segmentation
P. Bonizzoni, V. Brattka, B. Löwe (2013)
The Nature of Computation : Logic, Algorithms, Applications : 9th Conference on Computability in Europe, CiE 2013, Milan, Italy, July 1-5, 2013 : proceedingsLecture Notes in Computer Science, 7921
Local problems (1977-1983): independent set, vertex cover, dominating set, etc
Sharon Alpert, M. Galun, R. Basri, A. Brandt (2007)
Image Segmentation by Probabilistic Bottom-Up Aggregation and Cue Integration2007 IEEE Conference on Computer Vision and Pattern Recognition
K. Jain (1998)
A Factor 2 Approximation Algorithm for the Generalized Steiner Network ProblemCombinatorica, 21
M. Bateni, M. Hajiaghayi, D. Marx (2009)
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded TreewidthJ. ACM, 58
R. Ravi (1992)
Approximation Algorithms for Steiner Augmentations for Two-Connectivity
M. Resende, P. Pardalos (2006)
Handbook of Optimization in Telecommunications
Ioannis Giotis, V. Guruswami (2005)
Correlation clustering with a fixed number of clustersTheory Comput., 2
David Williamson, M. Goemans, M. Mihail, V. Vazirani (1993)
A primal-dual approximation algorithm for generalized steiner network problemsCombinatorica, 15
Shuchi Chawla, K. Makarychev, T. Schramm, G. Yaroslavtsev (2014)
Near Optimal LP Rounding Algorithm for CorrelationClustering on Complete and Complete k-partite GraphsProceedings of the forty-seventh annual ACM symposium on Theory of Computing
A. Galluccio, Guido Proietti (2002)
A Faster Approximation Algorithm for 2-Edge-Connectivity Augmentation
Cristopher Moore, S. Mertens (2011)
The Nature of Computation
Claire Mathieu, W. Schudy (2010)
Correlation clustering with noisy input
G. Borradaile, P. Klein (2008)
The Two-Edge Connectivity Survivable Network Problem in Planar Graphs
S. Khuller, U. Vishkin (1994)
Biconnectivity approximations and graph carvingsJ. ACM, 41
G. Frederickson, J. JáJá (1981)
Approximation Algorithms for Several Graph Augmentation ProblemsSIAM J. Comput., 10
Amir Alush, J. Goldberger (2013)
Break and Conquer: Efficient Correlation Clustering for Image Segmentation
A. Gionis, H. Mannila, Panayiotis Tsaparas (2005)
Clustering aggregation21st International Conference on Data Engineering (ICDE'05)
For every vertex u ∈ Q 1 ∩ Q 2 , let H be the concatenation of H ψ 1 (u) and H ψ 2 (u) at the vertex u. Update H by H ∪ {H }−{H ψ 1 (u) , H ψ 2 (u) }. Idem for every vertex u ∈ Q 1 ∩Q and for every
Vincent Cohen-Addad, Euiwoong Lee, Alantha Newman (2022)
Correlation Clustering with Sherali-Adams2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)
G. Even, J. Feldman, G. Kortsarz, Zeev Nutov (2009)
A 1.8 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2ACM Trans. Algorithms, 5
G. Kortsarz, Zeev Nutov (2007)
Approximating Minimum-Cost Connectivity Problems
N. Ailon, M. Charikar, Alantha Newman (2008)
Aggregating inconsistent information: Ranking and clusteringJ. ACM, 55
N. Ailon, Edo Liberty (2009)
Correlation Clustering Revisited: The "True" Cost of Error Minimization Problems
M. Charikar, V. Guruswami, Anthony Wirth (2003)
Clustering with qualitative information44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
G. Borradaile, P. Klein, Claire Mathieu (2009)
An O(n log n) approximation scheme for Steiner tree in planar graphsACM Trans. Algorithms, 5
Other problems (2012-2014): multiway cut, k-center
M. Goemans, A. Goldberg, Serge Plotkin, D. Shmoys, É. Tardos, David Williamson (1994)
Improved approximation algorithms for network design problems
Chaitanya Swamy (2004)
Correlation Clustering: maximizing agreements via semidefinite programming
N. Bansal, Avrim Blum, Shuchi Chawla (2002)
Correlation ClusteringMachine Learning, 56
H is initialized as H 1 ∪ H 2 ∪Ĥ, and I is initialized as I 1 ∪ I 2 ∪Î
Julian Yarkony, A. Ihler, Charless Fowlkes (2012)
Fast Planar Correlation Clustering for Image Segmentation
G. Borradaile, E. Demaine, Siamak Tazari (2009)
Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus GraphsAlgorithmica, 68
M. Bateni, M. Hajiaghayi, P. Klein, Claire Mathieu (2012)
A polynomial-time approximation scheme for planar multiway cut
Philip Klein, Claire Mathieu, Hang Zhou
Correlation Clustering and Two-edge-connected Augmentation for Planar Graphs * 1 Introduction 1.1 Correlation Clustering
E. Demaine, Dotan Emanuel, A. Fiat, Nicole Immorlica (2006)
Correlation clustering in general weighted graphsTheor. Comput. Sci., 361
Consider the forest F at the beginning of Step 3 of the construction. For every two-edge-connected component A in F, let H be the union of the subgraphs H a
David Martin, Charless Fowlkes, Jitendra Malik
Submitted to Ieee Transactions on Pattern Analysis and Machine Intelligence Learning to Detect Natural Image Boundaries Using Local Brightness, Color, and Texture Cues
A. Czumaj, A. Lingas (1999)
On approximability of the minimum-cost k-connected spanning subgraph problem
H. Nagamochi (1999)
An approximation for finding a smallest 2-edge-connected subgraph containing a specified spanning treeDiscret. Appl. Math., 126
G. Even, G. Kortsarz, Zeev Nutov (2011)
A 1.5-approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2Inf. Process. Lett., 111
Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
We study two problems. In correlation clustering, the input is a weighted graph, where every edge is labelled either ⟨+⟩\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\langle +\rangle $$\end{document} or ⟨-⟩\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\langle -\rangle $$\end{document} according to whether its endpoints are in the same category or in different categories. The goal is to produce a partition of the vertices into categories that tries to respect the labels of the edges. In two-edge-connected augmentation, the input is a weighted graph and a subset R of edges of the graph. The goal is to produce a minimum weight subset S of edges of the graph, such that for every edge in R, its endpoints are two-edge-connected in R∪S\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$R\cup S$$\end{document}. In this paper, we study these problems under the restriction that the input graph must be planar. We give an approximation-preserving reduction from correlation clustering on planar graphs to two-edge-connected augmentation on planar graphs. We give a polynomial-time approximation scheme (PTAS) for the latter problem, yielding a PTAS for the former problem as well. The approximation scheme employs brick decompositions, which have been used in previous approximation schemes for planar graphs, but the way it uses brick decompositions is fundamentally different from previous uses.
Algorithmica – Springer Journals
Published: Oct 1, 2023
Keywords: Correlation clustering; 2-edge-connected augmentation; Polynomial-time approximation scheme; Planar graphs
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.