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## Solving Pursuit-evasion Problems with Graph-Clear: an Overview

### Citations

102 | An annotated bibliography on guaranteed graph searching,
- Fomin, Thilikos
- 2008
(Show Context)
Citation Context ...guous strategies turn out to be simpler to compute [8], [13]. Yet, they are generally more expensive. For edge-searching imposing contiguity can increase the cost of the strategies almost by two-fold =-=[3]-=- and from [8] we can construct graphs for which there is also an increased cost for contiguity for Graph-Clear. An alternative graph-based pursuit-evasion model that can be applied in a robotic contex... |

67 | Capture of an intruder by mobile agents,
- Barriere, Flocchini, et al.
- 2002
(Show Context)
Citation Context ...vasion model that can be applied in a robotic context is edge-searching and the edge-searching variant with a node-located intruders as described in [4]. Applying weights to edge-searching as done in =-=[2]-=- then leads to graph model that also deals with large numbers of robots and multiple robots per action. The key differences between weighted edge-searching and GraphClear are in the requirements impos... |

49 | Visibility-based pursuit-evasion in an unknown planar environment.
- Sachs, LaValle, et al.
- 2004
(Show Context)
Citation Context ...ith its graph embedded. All weights in this example are equal to one. Connections between regions that are connected by edges are shown in black. The center region is the ”eagle” example redrawn from =-=[16]-=-. It can be cleared using the algorithm from [16] with only one robot and a simple gap sensor with sufficiently large range. During its execution it recontaminates the top part of the region and hence... |

25 | Pursuit-evasion on trees by robot teams
- Kolling, Carpin
(Show Context)
Citation Context ...by the team of robots? In our opinion, Graph-Clear finds one of its major strengths in the intuitive (yet powerful) answers it assumes for the above questions. II. STATE OF THE ART FOR GRAPH-CLEAR In =-=[13]-=- we give precise definitions for Graph-Clear. In summary, Graph-Clear is a problem defined on a surveillance graph. A surveillance graph is an undirected graph G = (V,E,w) where V is a set of vertices... |

20 | Multi-robot surveillance: An improved algorithm for the graph-clear problem.
- Kolling, Carpin
- 2008
(Show Context)
Citation Context ...connected subgraph. In some applications this provides the team with a safe and connected area in which one can move and deploy infrastructure. Contiguous strategies turn out to be simpler to compute =-=[8]-=-, [13]. Yet, they are generally more expensive. For edge-searching imposing contiguity can increase the cost of the strategies almost by two-fold [3] and from [8] we can construct graphs for which the... |

18 | Extracting surveillance graphs from robot maps.
- Kolling, Carpin
- 2008
(Show Context)
Citation Context ...graphs The question of how to obtain a graph representation is essential to any graph-model of pursuit-evasion if it should be applied to a robotic context. For Graph-Clear we presented heuristics in =-=[7]-=- and [5] that rely on a Voronoi Diagram to identify narrow parts of a two-dimensional environment. In general, the problem of identifying good graphs for an environment is difficult and depends on the... |

16 | Stealth tracking of an unpredictable target among obstacles,” in Algorithmic Foundations of Robotics
- Bandyopadhyay, Li, et al.
- 2004
(Show Context)
Citation Context ...hereas intruders have been often assumed to move randomly, stationary, or moving accordingly to unknown patterns. The other side of the game is no less interesting, but it has been scarcely addressed =-=[1]-=-, [14], [15] Not only there are many situations where it may be valuable to remain covert during the mission (wildlife observation, behind the lines operations, etc), but this may also shed some light... |

16 | The graph-clear problem: definition, theoretical properties and its connections to multirobot aided surveillance - Kolling, Carpin |

15 |
Verification and Control of Hybrid Systems
- Tabuada
- 2009
(Show Context)
Citation Context ...fications by design is of paramount importance. A fertile crossfertilization with hybrid systems theory seems to be the path to follow, even though only limited attempts have been reported up to now. =-=[17]-=-. • Interactive strategies. Strategies are generally global and pre-computed. Changes in the environment or agents that participate in the execution of a search schedule may cause unexpected change. A... |

9 | Multi robot pursuit evasion without maps
- Kolling, Carpin
- 2010
(Show Context)
Citation Context ... shows an example of a partitioning based on the Voronoi Diagram from [7] and the final graph extracted from it. Examples how to extract graphs while relying less on heuristics are presented in [11], =-=[12]-=-, and [5]. Therein an abstract sensor model, a sweep-line, is defined and robots are assumed to cover this line with sensors as it sweeps through and clears an environment. The surveillance graph is c... |

8 | Anytime guaranteed search using spanning trees,” The Robotics Institute,
- Hollinger, Kehagias, et al.
- 2008
(Show Context)
Citation Context ...r Graph-Clear. An alternative graph-based pursuit-evasion model that can be applied in a robotic context is edge-searching and the edge-searching variant with a node-located intruders as described in =-=[4]-=-. Applying weights to edge-searching as done in [2] then leads to graph model that also deals with large numbers of robots and multiple robots per action. The key differences between weighted edge-sea... |

6 | Probabilistic graph-clear,” in
- Kolling, Carpin
- 2009
(Show Context)
Citation Context ...egies on trees [8] in pseudo-polynomial; • suboptimal strategies on graphs from strategies on trees [6] in polynomial time; • extensions of previous algorithms to strategies for probabilistic actions =-=[10]-=- in polynomial time; • modification of Graph-Clear that requires a sweep to also prevent recontamination ( [5] Chapter 3). Hence, the problem of computing optimal contiguous strategies on trees in pol... |

5 | On weighted edge-searching
- Kolling, Carpin
- 2009
(Show Context)
Citation Context ...d edge-searching from [2] does not allow edge weights larger than the weight of the adjacent vertex. Finally, the algorithm presented in [2] turns out not be optimal for the weighted case as shown in =-=[9]-=-. A. Graph-Clear algorithms One of the major results we identified while studying Graph-Clear concerns its intrinsic computational hardness [13]. In its generality, for a given graph the problem of de... |

3 |
Surveillance strategies for target detection with sweep lines
- Kolling, Carpin
(Show Context)
Citation Context ...Fig. 2 shows an example of a partitioning based on the Voronoi Diagram from [7] and the final graph extracted from it. Examples how to extract graphs while relying less on heuristics are presented in =-=[11]-=-, [12], and [5]. Therein an abstract sensor model, a sweep-line, is defined and robots are assumed to cover this line with sensors as it sweeps through and clears an environment. The surveillance grap... |

3 | A cooperative distributed approach to target motion control in multirobot observation of multiple targets
- Markov, Carpin
- 2007
(Show Context)
Citation Context ...s intruders have been often assumed to move randomly, stationary, or moving accordingly to unknown patterns. The other side of the game is no less interesting, but it has been scarcely addressed [1], =-=[14]-=-, [15] Not only there are many situations where it may be valuable to remain covert during the mission (wildlife observation, behind the lines operations, etc), but this may also shed some light into ... |

2 |
Multi-Robot Pursuit-Evasion
- Kolling
- 2009
(Show Context)
Citation Context ...nomial time; • extensions of previous algorithms to strategies for probabilistic actions [10] in polynomial time; • modification of Graph-Clear that requires a sweep to also prevent recontamination ( =-=[5]-=- Chapter 3). Hence, the problem of computing optimal contiguous strategies on trees in polynomial time is solved. It is currently unclear whether one can compute non-contiguous strategies in polynomia... |

1 |
Enhancing self covertness in a hostile environment from expected observers at unknown locations
- Marzouqi, Jarvis
- 2006
(Show Context)
Citation Context ...uders have been often assumed to move randomly, stationary, or moving accordingly to unknown patterns. The other side of the game is no less interesting, but it has been scarcely addressed [1], [14], =-=[15]-=- Not only there are many situations where it may be valuable to remain covert during the mission (wildlife observation, behind the lines operations, etc), but this may also shed some light into the in... |