Affiliation:
1. Ben-Gurion University of the Negeb, Israel
Abstract
In this article, we study the classic
Weighted 3-Set
k
-Packing
problem: given a universe
U
, a family
\( {\mathcal {S}}\)
of subsets of size 3 of
U
, a weight function
\(w : {\mathcal {S}} \rightarrow \mathbb {R}\)
,
\(W \in \mathbb {R}\)
, and a parameter
\(k \in \mathbb {N}\)
, the objective is to decide if there is a subfamily
\( {\mathcal {S}}\)
′
⊆
\( {\mathcal {S}}\)
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Theory and Mathematics,Theoretical Computer Science