A Simple 2 -Approximation for Maximum-Leaf Spanning Tree
Journal
International Journal of Foundations of Computer Science
Date Issued
2023-01-01
Author(s)
Liao, I. Cheng
HSUEH-I LU
Abstract
For an m-edge connected simple graph G, finding a spanning tree of G with the maximum number of leaves is MAXSNP-complete. The problem remains NP-complete even if G is planar and the maximal degree of G is at most four. Lu and Ravi gave the first known polynomial-time approximation algorithms with approximation factors 5 and 3. Later, they obtained a 3-approximation algorithm that runs in near-linear time. The best known result is Solis-Oba, Bonsma, and Lowski's O(m)-time 2-approximation algorithm. We show an alternative simple O(m)-time 2-approximation algorithm whose analysis is simpler. This paper is dedicated to the cherished memory of our dear friend, Professor Takao Nishizeki.
Subjects
Approximation algorithms | maximum-leaf spanning tree; Computer Science - Data Structures and Algorithms; Computer Science - Data Structures and Algorithms; 05C38, 05C10, 05C85, 68P05
Description
10 pages, 4 figures
Type
journal article