Approximation algorithms for connected maximum cut and related problems

Mohammad Taghi Hajiaghayi; Guy Kortsarz; Robert Macdavid; Manish Purohit; Kanthi Sarpatwar

doi:10.1007/978-3-662-48350-3_58

Approximation algorithms for connected maximum cut and related problems

Mohammad Taghi Hajiaghayi, Guy Kortsarz, Robert Macdavid, Manish Purohit, Kanthi Sarpatwar

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first nontrivial (Formula presented) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.

Original language	English
Title of host publication	Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings
Editors	Nikhil Bansal, Irene Finocchi
Publisher	Springer Verlag
Pages	693-704
Number of pages	12
ISBN (Print)	9783662483497
DOIs	https://doi.org/10.1007/978-3-662-48350-3_58
State	Published - 2015
Externally published	Yes
Event	23rd European Symposium on Algorithms, ESA 2015 - Patras, Greece Duration: 14 Sep 2015 → 16 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9294
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	23rd European Symposium on Algorithms, ESA 2015
Country/Territory	Greece
City	Patras
Period	14/09/15 → 16/09/15

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

Access to Document

10.1007/978-3-662-48350-3_58

Cite this

Hajiaghayi, M. T., Kortsarz, G., Macdavid, R., Purohit, M., & Sarpatwar, K. (2015). Approximation algorithms for connected maximum cut and related problems. In N. Bansal, & I. Finocchi (Eds.), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings (pp. 693-704). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_58

Hajiaghayi, Mohammad Taghi ; Kortsarz, Guy ; Macdavid, Robert et al. / Approximation algorithms for connected maximum cut and related problems. Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. editor / Nikhil Bansal ; Irene Finocchi. Springer Verlag, 2015. pp. 693-704 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V,E) and the goal is to find a subset of vertices S ⊆ V that maximizes the number of edges in the cut δ(S) such that the induced graph G[S] is connected. We present the first nontrivial (Formula presented) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in stark contrast to the classical max-cut problem, we show that the connected maximum cut problem remains NP-hard even on unweighted, planar graphs. On the positive side, we obtain a polynomial time approximation scheme for the connected maximum cut problem on planar graphs and more generally on graphs with bounded genus.",

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Hajiaghayi, MT, Kortsarz, G, Macdavid, R, Purohit, M & Sarpatwar, K 2015, Approximation algorithms for connected maximum cut and related problems. in N Bansal & I Finocchi (eds), Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9294, Springer Verlag, pp. 693-704, 23rd European Symposium on Algorithms, ESA 2015, Patras, Greece, 14/09/15. https://doi.org/10.1007/978-3-662-48350-3_58

Approximation algorithms for connected maximum cut and related problems. / Hajiaghayi, Mohammad Taghi; Kortsarz, Guy; Macdavid, Robert et al.
Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. ed. / Nikhil Bansal; Irene Finocchi. Springer Verlag, 2015. p. 693-704 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9294).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Hajiaghayi MT, Kortsarz G, Macdavid R, Purohit M, Sarpatwar K. Approximation algorithms for connected maximum cut and related problems. In Bansal N, Finocchi I, editors, Algorithms – ESA 2015 - 23rd Annual European Symposium, Proceedings. Springer Verlag. 2015. p. 693-704. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-48350-3_58

Approximation algorithms for connected maximum cut and related problems

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