# 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} }

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

### Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree

- Mathematics, Computer ScienceIPEC
- 2020

A heapable sequence is a sequence of numbers that can be arranged in a min-heap data structure. Finding a longest heapable subsequence of a given sequence was proposed by Byers, Heeringa,…

### On the heapability of finite partial orders

- Mathematics, Computer ScienceDiscret. Math. Theor. Comput. Sci.
- 2020

A characterization result reminiscent of the proof of Dilworth's theorem is proved, which yields as a byproduct a flow-based algorithm for computing such a minimal decomposition of sets and sequences of intervals.

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