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

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Abstract

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 (8.097k ), 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 (12.155k ) 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.

Original languageEnglish
Article number6
JournalACM Transactions on Computation Theory
Volume15
Issue number3-4
DOIs
StatePublished - 12 Dec 2023

Keywords

  • 3-set k-packing
  • P-packing
  • Representative sets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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