TY - JOUR

T1 - Approximation algorithms for connected maximum cut and related problems

AU - Hajiaghayi, Mohammad Taghi

AU - Kortsarz, Guy

AU - MacDavid, Robert

AU - Purohit, Manish

AU - Sarpatwar, Kanthi

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/4/24

Y1 - 2020/4/24

N2 - 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 non-trivial Ω([Formula presented]) approximation algorithm for the Connected Maximum Cut problem in general graphs using novel techniques. We then extend our algorithm to edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in contrast to the classical Max-Cut problem that can be solved in polynomial time on planar graphs, we show that the Connected Maximum Cut problem remains NP-hard 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 bounded genus graphs.

AB - 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 non-trivial Ω([Formula presented]) approximation algorithm for the Connected Maximum Cut problem in general graphs using novel techniques. We then extend our algorithm to edge weighted case and obtain a poly-logarithmic approximation algorithm. Interestingly, in contrast to the classical Max-Cut problem that can be solved in polynomial time on planar graphs, we show that the Connected Maximum Cut problem remains NP-hard 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 bounded genus graphs.

KW - Approximation algorithms

KW - Connected maximum cut

KW - Connected submodular maximization

UR - http://www.scopus.com/inward/record.url?scp=85078757980&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2020.01.016

DO - 10.1016/j.tcs.2020.01.016

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AN - SCOPUS:85078757980

SN - 0304-3975

VL - 814

SP - 74

EP - 85

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -