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We consider the following distributed pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown $n$-node network. Their goal is to execute a search strategy that guarantees capturing a fast…

Discrete Mathematics · Computer Science 2021-01-19 Dariusz Dereniowski , Dorota Urbańska

In this paper, we consider the problem of exploring unknown environments with autonomous agents. We model the environment as a graph with edge weights and analyze the task of visiting all vertices of the graph at least once. The hardness of…

Computational Complexity · Computer Science 2016-11-04 Hans-Joachim Böckenhauer , Janosch Fuchs , Ulla Karhumäki , Walter Unger

We present results on new variants of the famous linear search (or cow-path) problem that involves an agent searching for a target with unknown position on the infinite line. We consider the variant where the agent can move either at speed…

Discrete Mathematics · Computer Science 2025-05-15 Jared Coleman , Oscar Morales-Ponce

Consider search on an infinite line involving an autonomous robot starting at the origin of the line and an oblivious moving target at initial distance $d \geq 1$ from it. The robot can change direction and move anywhere on the line with…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-08 Jared Coleman , Evangelos Kranakis , Danny Krizanc , Oscar Morales-Ponce

Due to some significantly contradicting research results, we reconsider the problem of the online exploration of a simple grid cell environment. In this model an agent attains local information about the direct four-neigbourship of a…

Computational Geometry · Computer Science 2024-07-25 Maximilian Brock , Martin Brückmann , Elmar Langetepe , Raphael Wude

In environments with scarce resources, adopting the right search strategy can make the difference between succeeding and failing, even between life and death. At different scales, this applies to molecular encounters in the cell cytoplasm,…

Biological Physics · Physics 2018-09-27 Giorgio Volpe , Giovanni Volpe

We consider the problem of minimizing the worst-case search time for a hidden point target in the plane using multiple mobile agents of differing speeds, all starting from a common origin. The search time is normalized by the target's…

Data Structures and Algorithms · Computer Science 2026-02-02 Konstantinos Georgiou , Caleb Jones , Matthew Madej

A single target is hidden at a location chosen from a predetermined probability distribution. Then, a searcher must find a second probability distribution from which random search points are sampled such that the target is found in the…

Data Analysis, Statistics and Probability · Physics 2013-05-29 Joseph Snider

We address the problem where a mobile search agent seeks to find an unknown number of stationary objects distributed in a bounded search domain, and the search mission is subject to time/distance constraint. Our work accounts for false…

Robotics · Computer Science 2018-06-26 Harun Yetkin , Collin Lutz , Daniel Stilwell

Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the…

Combinatorics · Mathematics 2016-09-06 Avrim Blum , Prasad Chalasani

We consider the problem of exploring an unknown tree with a team of $k$ initially colocated mobile agents. Each agent has limited energy and cannot, as a result, traverse more than $B$ edges. The goal is to maximize the number of nodes…

Data Structures and Algorithms · Computer Science 2018-02-20 Evangelos Bampas , Jérémie Chalopin , Shantanu Das , Jan Hackfeld , Christina Karousatou

We introduce and study the problem of planning a trajectory for an agent to carry out a scouting mission while avoiding being detected by an adversarial guard. This introduces an adversarial version of classical visibility-based planning…

Robotics · Computer Science 2019-02-26 Zhongshun Zhang , Yoonchang Sung , Lifeng Zhou , Jonathon M. Smereka , Joseph Lee , Pratap Tokekar

A mobile agent has to reach a target in the Euclidean plane. Both the agent and the target are modeled as points. In the beginning, the agent is at distance at most $D>0$ from the target. Reaching the target means that the agent gets at a…

Data Structures and Algorithms · Computer Science 2017-10-20 Andrzej Pelc

The linear search problem, informally known as the cow path problem, is one of the fundamental problems in search theory. In this problem, an immobile target is hidden at some unknown position on an unbounded line, and a mobile searcher,…

Data Structures and Algorithms · Computer Science 2020-09-15 Spyros Angelopoulos

In this paper, we study the problem of exploring an unknown Region Of Interest (ROI) with a team of aerial robots. The size and shape of the ROI are unknown to the robots. The objective is to find a tour for each robot such that each point…

Robotics · Computer Science 2022-04-18 Yoonchang Sung , Deeksha Dixit , Pratap Tokekar

We consider a perimeter defense problem in a rooted full tree graph environment in which a single defending vehicle seeks to defend a set of specified vertices, termed as the perimeter from mobile intruders that enter the environment…

Systems and Control · Electrical Eng. & Systems 2025-02-11 Richard L. Frost , Shaunak D. Bopardikar

There are $n\geq 3$ unit speed mobile agents placed at the origin of the infinite line. In as little time as possible, the agents must find and evacuate from an exit placed at an initially unknown location on the line. The agents can…

Data Structures and Algorithms · Computer Science 2026-05-12 J. Czyzowicz , R. Killick , E. Kranakis , G. Stachowiak

In the event of a total loss of thrust, a pilot must identify a reachable landing site and subsequently execute a forced landing. To do so, they must estimate which region on the ground can be reached safely in gliding flight. We call this…

Optimization and Control · Mathematics 2024-07-30 Giovanni Piccioli

We consider the problem of multiple agents or robots searching for a target in the plane. This is motivated by Search and Rescue operations (SAR) in the high seas which in the past were often performed with several vessels, and more…

Robotics · Computer Science 2015-06-26 Alejandro Lopez-Ortiz , Daniela Maftuleac

Optimal search strategies where targets are observed at several different angles are found. Targets are assumed to exhibit rectangular symmetry and have a uniformly-distributed orientation. By rectangular symmetry, it is meant that one side…

Optimization and Control · Mathematics 2011-06-06 François-Alex Bourque , Bao U. Nguyen