Improved approximation algorithms for weighted 2-path partitions

Combining this algorithm with a previously known approximation algorithm for the 3-Set Packing problem, we obtain a .6-approximation algorithm for the problem of partitioning a {0,1}-edge-weighted graph into k vertex disjoint triangles of maximum total weight. The best known approximation algorithm for general weights is due to Chen and Tanahashi (2009) and achieves an approximation ratio of .5257.