Concetti Chiave
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.
Sintesi
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.