APPROXIMATING THE SPANNING k-TREE FOREST PROBLEM
Chung-Shou Liao, Louxin Zhang · International Journal of Foundations of Computer Science · 2012
The spanning star forest problem is an interesting algorithmic problem in combinatorial optimization and finds different applications. We generalize it into the spanning k-tree forest problem, which is to find a maximum spanning forest in which each tree component has a central vertex and other vertices in the component have distance at most k away from the central vertex. We show that this new problem can be approximated with ratio [Formula: see text] in polynomial time for both undirected and directed graphs. In the weighted distance model, a ½-approximation algorithm is presented for it.