A Simple 2-Approximation for Maximum-Leaf Spanning Tree

03/06/2023

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by   I-Cheng Liao, et al.

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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.