A 3/2-APPROXIMATION ALGORITHM FOR FINDING SPANNING TREES WITH MANY LEAVES IN CUBIC GRAPHS

作者：Bonsma Paul^*; Zickfeld Florian

来源：SIAM Journal on Discrete Mathematics, 2011, 25(4): 1652-1666.

DOI：10.1137/100801251

• maximum leaf
• spanning tree
• connected dominating set
• cubic graph
• approximation algorithm

We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter x(G) and construct a tree with at least (n - x(G) + 4)/3 leaves, and we prove that no tree with more than (n- x(G)+ 2)/2 leaves exists. In contrast to previous approximation algorithms for MaxLeaf, our algorithm works with connected dominating sets instead of by constructing a tree directly. The algorithm also yields a 4/3-approximation for the minimum connected dominating set problem in cubic graphs.

• 出版日期2011