# The Maximum Binary Tree Problem

@article{Chandrasekaran2019TheMB,
title={The Maximum Binary Tree Problem},
author={Karthekeyan Chandrasekaran and Elena Grigorescu and Gabriel Istrate and Shubhang Kulkarni and Young-San Lin and Minshen Zhu},
journal={Algorithmica},
year={2019},
volume={83},
pages={2427 - 2468}
}
• Published 17 September 2019
• Computer Science, Mathematics
• Algorithmica
We introduce and investigate the approximability of the maximum binary tree problem (MBT) in directed and undirected graphs. The goal in MBT is to find a maximum-sized binary tree in a given graph. MBT is a natural variant of the well-studied longest path problem, since both can be viewed as finding a maximum-sized tree of bounded degree in a given graph. The connection to longest path motivates the study of MBT in directed acyclic graphs (DAGs), since the longest path problem is solvable…
2 Citations

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## References

SHOWING 1-10 OF 54 REFERENCES

• Mathematics
Discret. Appl. Math.
• 1987
• Mathematics
ICALP
• 2004
It is shown that neither the longest path and the longest cycle in directed graphs on n vertices can be polynomial time approximated within n 1 − − e for any e> 0 unless P=NP.
• Mathematics, Computer Science
Algorithmica
• 2006
It is shown that, for any ε<1, the problem of finding a path of lengthn-nε in ann-vertex Hamiltonian graph is NP-hard, and it is conjectured that the result can be strengthened to say that,for some constant δ>0, finding an approximation of rationδ is alsoNP-hard.
• Mathematics, Computer Science
ANALCO
• 2011
An efficient algorithm is obtained for determining the heapability of a sequence, and it is proved that the question of whether a sequence can be arranged in a complete binary heap is NP-hard.
• Mathematics
Discret. Appl. Math.
• 2005
• Computer Science
Math. Oper. Res.
• 1993
We present a polynomial-time approximation algorithm with worst-case ratio 7/6 for the special case of the traveling salesman problem in which all distances are either one or two. We also show that
• Mathematics
DCFS
• 2016
We outline results and open problems concerning partitioning of integer sequences and partial orders into heapable subsequences (previously defined and established by Byers et al.).
• Mathematics, Computer Science
SIAM J. Comput.
• 2009
This work presents polynomial-time approximation algorithms for some degree-bounded directed network design problems and gives the first additive $O(1)$-approximation guarantee for degree- bounded intersecting/crossing supermodular connectivity problems.