Core Concepts
We present a simple and efficient O(m)-time 2-approximation algorithm for the maximum-leaf spanning tree problem, which is NP-complete even for planar graphs with maximum degree 4.
Abstract
The paper presents a simple and efficient 2-approximation algorithm for the maximum-leaf spanning tree problem. The key highlights are:
The algorithm has a single simple loop that can be implemented to run in O(m) time using basic data structures like arrays and linked lists.
The proof for the 2-approximation ratio is shorter and simpler compared to the previous best known 2-approximation algorithm.
The algorithm follows a greedy approach, expanding the tree in each round to maximize the number of leaves. If a round cannot increase the number of leaves, it looks ahead one round and attempts to maximize the number of leaves in two consecutive rounds.
When no suitable expansion vertices can be found for two consecutive rounds, the algorithm employs a "depth-first" expansion strategy to simplify the analysis of the approximation ratio.
The analysis shows that the approximation ratio is tight by providing an example where the algorithm returns a spanning tree with half the number of leaves as the optimal spanning tree.