On maximum leaf trees and connections to connected maximum cut problems

Rajiv Gandhi, Mohammad Taghi Hajiaghayi, Guy Kortsarz, Manish Purohit, Kanthi Sarpatwar

Research output: Contribution to journalArticlepeer-review


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/log⁡n) 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/log2⁡n) (Hajiaghayi et al., ESA 2015) to Ω(1/log⁡n).

Original languageEnglish
Pages (from-to)31-34
Number of pages4
JournalInformation Processing Letters
StatePublished - Jan 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.


  • Approximation algorithms
  • Connected maximum cut
  • Maximum leaf trees


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