Forgetfulness Can Make You Faster: An O^∗(8.097^k)-time Algorithm for Weighted 3-set k-packing

In this article, we study the classic Weighted 3-Set k-Packing problem: given a universe U, a family S of subsets of size 3 of U, a weight function w : S → R, W ∈ R, and a parameter k ∈ N, the objective is to decide if there is a subfamily S ^´ ⊆ S of k disjoint sets and total weight at least W . We present a deterministic parameterized algorithm for this problem that runs in time O^∗ (8.097^k ), where O^∗ hides factors polynomial in the input size. This substantially improves upon the previously best deterministic algorithm for Weighted 3-Set k-Packing, which runs in time O^∗ (12.155^k ) SIDMA [18], and was also the best deterministic algorithm for the unweighted version of this problem. Our algorithm is based on a novel application of the method of representative sets that might be of independent interest.