Emergent Mind
ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs
(2403.11426)
Published Mar 18, 2024
in
cs.DS
and
cs.CG
Abstract
In this paper, we consider the Cycle Packing problem on unit disk graphs defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of $k$ vertex-disjoint cycles of G if it exists. Our algorithm runs in time $2{O(\sqrt k)}n{O(1)}$. This improves the $2{O(\sqrt k\log k)}n{O(1)}$-time algorithm by Fomin et al. [SODA 2012, ICALP 2017]. Moreover, our algorithm is optimal assuming the exponential-time hypothesis.
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