TY - JOUR

T1 - On maximum leaf trees and connections to connected maximum cut problems

AU - Gandhi, Rajiv

AU - Hajiaghayi, Mohammad Taghi

AU - Kortsarz, Guy

AU - Purohit, Manish

AU - Sarpatwar, Kanthi

N1 - Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2018/1

Y1 - 2018/1

N2 - In an instance of the (directed) Max Leaf Tree (MLT) problem we are given a vertex-weighted (di)graph G(V,E,w) and the goal is to compute a subtree with maximum weight on the leaves. The weighted Connected Max Cut (CMC) problem takes in an undirected edge-weighted graph G(V,E,w) and seeks a subset S⊆V such that the induced graph G[S] is connected and ∑e∈δ(S)w(e) is maximized. We obtain a constant approximation algorithm for MLT when the weights are chosen from {0,1}, which in turn implies a Ω(1/logn) approximation for the general case. We show that the MLT and CMC problems are related and use the algorithm for MLT to improve the factor for CMC from Ω(1/log2n) (Hajiaghayi et al., ESA 2015) to Ω(1/logn).

AB - In an instance of the (directed) Max Leaf Tree (MLT) problem we are given a vertex-weighted (di)graph G(V,E,w) and the goal is to compute a subtree with maximum weight on the leaves. The weighted Connected Max Cut (CMC) problem takes in an undirected edge-weighted graph G(V,E,w) and seeks a subset S⊆V such that the induced graph G[S] is connected and ∑e∈δ(S)w(e) is maximized. We obtain a constant approximation algorithm for MLT when the weights are chosen from {0,1}, which in turn implies a Ω(1/logn) approximation for the general case. We show that the MLT and CMC problems are related and use the algorithm for MLT to improve the factor for CMC from Ω(1/log2n) (Hajiaghayi et al., ESA 2015) to Ω(1/logn).

KW - Approximation algorithms

KW - Connected maximum cut

KW - Maximum leaf trees

UR - http://www.scopus.com/inward/record.url?scp=85029579591&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2017.06.002

DO - 10.1016/j.ipl.2017.06.002

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AN - SCOPUS:85029579591

SN - 0020-0190

VL - 129

SP - 31

EP - 34

JO - Information Processing Letters

JF - Information Processing Letters

ER -