An O∗(3.533k)-time parameterized algorithm for the 3-set packing problem

A parameterized algorithm for the well-known NP-complete problem 3-set packing is presented. The algorithm is based on the following new approaches: (1) an efficient algorithm for problem instances in which one element is known for each of the 3-sets in a solution packing (i.e., type-1 instances); (2) an efficient algorithm for problem instances in which at least two elements are known for each of the 3-sets in a solution packing (i.e., type-2 instances); and (3) an effective decomposition of a general instance of 3-set packing into two instances of type-1 and type-2, respectively, whose base sets are disjoint. This technique results in an improved parameterized algorithm of running time O∗(3.533k) for the 3-set packing problem, improving the previous best upper bound O∗(4.613k).