Randomized Pursuit-Evasion in Graphs

@article{Adler2003RandomizedPI,
  title={Randomized Pursuit-Evasion in Graphs},
  author={Micah Adler and Harald R{\"a}cke and Naveen Sivadasan and Christian Sohler and Berthold V{\"o}cking},
  journal={Combinatorics, Probability and Computing},
  year={2003},
  volume={12},
  pages={225 - 244}
}
We analyse a randomized pursuit-evasion game played by two players on a graph, a hunter and a rabbit. Let $G$ be any connected, undirected graph with $n$ nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be restricted to the graph $G$: in every round, the hunter can move using at most one edge. For the… 

A Study on a Game of Pursuit and Evasion on a Cycle Graph

The Hunter vs Rabbit game on graph is analyzed, a formalization of strategies using a random walk, theoretical estimation of bounds of a probability the rabbit caught, and computing simulation results are introduced.

A property of random walks on a cycle graph

A formalization of strategies using a random walk, theoretical estimation of bounds of a probability that the hunter catches the rabbit, and computing simulation results are introduced.

A property of randomwalks on a cycle graph

A formalization of strategies using a random walk, theoretical estimation of bounds of a probability that the hunter catches the rabbit, and computing simulation results are introduced that help choose the parameter β of a rabbit strategy according to the size N of the given graph.

Randomized pursuit-evasion with limited visibility

It is shown that two hunters suffice for catching rabbits with limited visibility with high probability, and polynomial time algorithms are presented that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G.

How to Hunt an Invisible Rabbit on a Graph

Locating a robber with multiple probes

The role of information in the cop-robber game

Monte Carlo Tree Search for the Hide-and-Seek Game Scotland Yard

This paper describes how Monte Carlo tree search (MCTS) can be applied to the hide-and-seek game Scotland Yard, and proposes a new technique, called location categorization, that biases the possible locations of the hider.

Online problems and two-player games: algorithms and analysis

This thesis studies three problems that are adversarial in nature, and presents a probabilistic analysis of the well-known text book algorithm called the work function algorithm, which reveals that the performance of this algorithm is much better than worst-case for a large class of inputs.

Hunter, Cauchy Rabbit, and Optimal Kakeya Sets

A planar set that contains a unit segment in every direction is called a Kakeya set. We relate these sets to a game of pursuit on a cycle Zn. A hunter and a rabbit move on the nodes of Zn without
...

References

SHOWING 1-10 OF 27 REFERENCES

The complexity of searching a graph

It is shown that determining whether s(G) ≤ K, for a given integer K, is NP-hard for general graphs but can be solved in linear time for trees.

Search Games with Mobile and Immobile Hider

We consider search games in which the searcher moves along a continuous trajectory in a set Q until he captures the hider, where Q is either a network or a two (or more) dimensional region. We

Recontamination does not help to search a graph

This paper proves that every graph can be searched using a minimum number of searchers without this recontamination occurring, that is, without clearing any edge twice, and places the graph-searching problem in NP, completing the proof by Megiddo et al. that theGraph searching problem is NP-complete.

Random walks, universal traversal sequences, and the complexity of maze problems

Results are derived suggesting that the undirected reachability problem is structurally different from, and easier than, the directed version of NSPACE(logn), an affirmative answer to a question of S. Cook.

Eavesdropping games: a graph-theoretic approach to privacy in distributed systems

This work combinatorially characterize and compare privacy maintenance problems, determine their feasibility (under numerous bug models), suggest protocols for the feasible cases, and analyze their computational complexity.

Searching and Pebbling

An Experimental Study of Basic Communication Protocols in Ad-hoc Mobile Networks

The experiments showed that for both protocols only a small support is required for efficient communication, and that the runners protocol outperforms the snake protocol in almost all types of mobile networks the authors considered.

An efficient communication strategy for ad-hoc mobile networks

A simple, correct and efficient protocol that manages to establish communication between any pair of mobile hosts in small, a-priori guaranteed expected time bounds even in the worst case of arbitrary motions of the hosts that not in the support.

A Visibility-Based Pursuit-Evasion Problem

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is

Sweeping simple polygons with a chain of guards

The notion of the “link width” of a polygon, which is a key component of the O(n log n)-time approximation algorithm, is introduced, which may have independent interest, as it captures important structural properties of simple polygons.