Hunting a rabbit: complexity, approximability and some characterizations
Walid Ben-Ameur, Harmender Gahlawat, Alessandro Maddaloni

TL;DR
This paper investigates the computational complexity of the Hunters and Rabbit game, proving NP-hardness of calculating the hunting number, and provides approximation algorithms and characterizations for specific graph classes.
Contribution
It establishes NP-hardness results for computing the hunting number, introduces approximation algorithms, and characterizes graphs with hunting number one.
Findings
Computing the hunting number is NP-hard for bipartite graphs.
Approximation algorithms achieve an $l$-factor within polynomial time.
Polynomial-time solution for bipartite graphs with two time slots.
Abstract
In the Hunters and Rabbit game, hunters attempt to shoot an invisible rabbit on a given graph . In each round, the hunters select vertices to shoot at, while the rabbit moves along an edge of . The hunters win if, at any point, the rabbit is shot. The hunting number of , denoted , is the minimum integer such that hunters have a winning strategy regardless of the rabbit's moves. The computational complexity of determining has been one of the longest-standing open questions about the game. Our first main contribution resolves this by proving that computing is NP-hard, even for bipartite simple graphs. We further show that the problem remains NP-hard even when or when , where is the order of . In addition, we prove that it is NP-hard to approximate additively within…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Artificial Intelligence in Games
