The Maximum Binary Tree Problem

  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},
  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

Figures from this paper

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

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

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.



Bipartite permutation graphs

Approximating Longest Directed Paths and Cycles

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.

On approximating the longest path in a graph

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.

Heapable Sequences and Subsequences

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.

Degree constrained subgraphs

The Traveling Salesman Problem with Distances One and Two

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

Heapability, Interactive Particle Systems, Partial Orders: Results and Open Problems

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.).

Additive Guarantees for Degree-Bounded Directed Network Design

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.

Subgraphs of minimal degree k