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ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs: Optimizing Cycle Packing Problem with Improved Algorithm

Core Concepts
Optimizing the Cycle Packing problem on unit disk graphs with an improved algorithm.
The paper discusses the Cycle Packing problem on unit disk graphs, presenting an algorithm that aims to find a set of k vertex-disjoint cycles of G. It improves upon previous algorithms by running in 2O(√k)nO(1) time and is optimal under the exponential-time hypothesis. The study focuses on parameterized algorithms and approximation algorithms for various graph classes, particularly unit disk graphs. The content delves into geometric tools, surface decomposition, and weighted cycle separators for planar graphs.
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. The algorithm runs in time 2O(√k)nO(1). For planar graphs, a 2/3-balanced cycle separator can be computed with desired cycle-weight.
"In this paper, we present an ETH-tight parameterized algorithm for the Cycle Packing problem on unit disk graphs." - Shinwoo An "Our algorithm runs in time 2O(√k)nO(1) and is optimal assuming the exponential-time hypothesis." - Eunjin Oh

Key Insights Distilled From

by Shinwoo An,E... at 03-19-2024
ETH-Tight Algorithm for Cycle Packing on Unit Disk Graphs

Deeper Inquiries

How does the proposed algorithm compare to existing methods for solving the Cycle Packing problem


What are the implications of optimizing cycle packing algorithms for real-world applications


How can these findings be extended to other types of graph problems beyond unit disk graphs