### Citations

426 | The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd edition - Knuth - 1997 |

122 | A game of cops and robbers
- Aigner, Fromme
- 1984
(Show Context)
Citation Context .... In the discrete problem the cops and the robber traverse (at most) one edge of a graph simultaneously with each tick of the clock. (The discrete problem considered here differs from that studied by =-=[1]-=-, [26], and others because in their formulation the cops move adaptively, not on fixed routes.) In the continuous problem, the cops and the robber have the same maximum speed and move continuously in ... |

120 |
Di¤erential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization
- Isaacs
- 1965
(Show Context)
Citation Context ... all by the other? What does “capture” mean? Are the man’s and the lion’s moves simultaneous or in alternation? The literature of pursuit/evasion games is much too broad to be summarized here: Isaacs =-=[15]-=- is a classic, though now dated reference; some historical information can be found in Nahin [25]. We give only a smattering of references, together with details of the results particularly relevant t... |

90 | A mathematician’s Miscellany - Littlewood - 1953 |

68 |
Vertex-to-vertex pursuit in a graph
- Nowakowski, Winkler
(Show Context)
Citation Context ...the discrete problem the cops and the robber traverse (at most) one edge of a graph simultaneously with each tick of the clock. (The discrete problem considered here differs from that studied by [1], =-=[26]-=-, and others because in their formulation the cops move adaptively, not on fixed routes.) In the continuous problem, the cops and the robber have the same maximum speed and move continuously in a cont... |

67 |
and Screening: General Principles with Historical Applications
- Koopman, Search
- 1980
(Show Context)
Citation Context ... results particularly relevant to this paper. Pursuit problems have been studied at least since the seventeenth century, and became especially popular during and after World War II (see, for example, =-=[19]-=- or [24]) but the lion-and-man style problems date from a problem posed by Tibor Radó (as given in Littlewood [22, pp. 114–117]): a lion and man move around in the interior of a circle; both move cont... |

42 | Compressions and isoperimetric inequalities - Bollobás, Leader - 1991 |

37 |
Methods of Operations Research
- Kimball
- 1951
(Show Context)
Citation Context ... particularly relevant to this paper. Pursuit problems have been studied at least since the seventeenth century, and became especially popular during and after World War II (see, for example, [19] or =-=[24]-=-) but the lion-and-man style problems date from a problem posed by Tibor Radó (as given in Littlewood [22, pp. 114–117]): a lion and man move around in the interior of a circle; both move continuously... |

36 |
Lattice Points
- Krätzel
- 1988
(Show Context)
Citation Context ...emmas, proved in Appendix A, that count the numbers of grid vertices (lattice points) with certain distance properties; although there is a considerable literature on such problems (see, for example, =-=[20]-=-), we have found nothing useful to our context. For a point p of the plane, be the set of grid vertices in an open disk not necessarily a grid vertex, let Dr p of radius r centered at p; that is, Dr p... |

34 |
Solution of David Gale's Lion and Man problem
- Sgall
- 2001
(Show Context)
Citation Context ...ure indefinitely. Variations have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], [11], Gale (see Guy [13]) and Sgall =-=[28]-=-, Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit by a robot [14]... |

23 | Unsolved Problems in Combinatorial Games
- Guy, Nowakowski
- 2011
(Show Context)
Citation Context ...as to avoid capture indefinitely. Variations have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], [11], Gale (see Guy =-=[13]-=-) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit... |

15 |
Sur les correspondances multivoques des ensembles
- Konig
- 1926
(Show Context)
Citation Context ...aving at least ⌊n 2 /2⌋ outcomes at every level. We can form a decision tree of safe moves for the robber by connecting a root to the accessible positions at time 0 and use the König “infinity lemma” =-=[18]-=- (see [17, sec. 2.3.4.3]) to show that such tree has an infinite path. 2 Note that the proof remains valid even if the cops can jump great distances! 3 The Continuous Problem In the continuous version... |

13 | Efficient cooperative search of smart targets using uav swarms
- Altshuler, Yanovsky, et al.
(Show Context)
Citation Context ...lovitch Besicovitch to show that the man can move so as to avoid capture indefinitely. Variations have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein =-=[3]-=-, Croft [7], Flynn [9], [10], [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usual... |

11 |
Chases and Escapes: The Mathematics of Pursuit and Evasion
- Nahin
- 2007
(Show Context)
Citation Context ...n alternation? The literature of pursuit/evasion games is much too broad to be summarized here: Isaacs [15] is a classic, though now dated reference; some historical information can be found in Nahin =-=[25]-=-. We give only a smattering of references, together with details of the results particularly relevant to this paper. Pursuit problems have been studied at least since the seventeenth century, and beca... |

8 |
Pursuit-evasion with imprecise target location
- Rote
- 2003
(Show Context)
Citation Context ...anovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote =-=[27]-=-. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit by a robot [14]), the version we consider is more naturally described as a robber evading cops on patrol. Specific... |

6 |
The homicidal chauffeur
- Merz
- 1974
(Show Context)
Citation Context ...], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz =-=[23]-=-, and Rote [27]. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit by a robot [14]), the version we consider is more naturally described as a robber evading cops on p... |

5 |
The complexity of pursuit on a graph. Theor
- Goldstein, Reingold
- 1995
(Show Context)
Citation Context ...have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold =-=[12]-=-, Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit by a robot [14]), the version we consider is... |

4 | How many lions can one man avoid
- Berger, Grüne, et al.
- 2007
(Show Context)
Citation Context ...a robber can evade on either an n × n discrete grid or on an n × n (continuous) square region? Among other results, they proved that Ω( √ n) cops can be evaded in either case. Berger, Grüne and Klein =-=[4]-=- improved this result to ⌊n/2⌋ cops in the discrete case, as well as giving a variety of results for higher dimensions. Finally, Brass, Kim, Na, and Shin [6] showed that if the cops and robber move in... |

4 |
Escaping offline searchers and isoperimetric theorems
- Brass, Kim, et al.
(Show Context)
Citation Context ...ed in either case. Berger, Grüne and Klein [4] improved this result to ⌊n/2⌋ cops in the discrete case, as well as giving a variety of results for higher dimensions. Finally, Brass, Kim, Na, and Shin =-=[6]-=- showed that if the cops and robber move in alternation on the n × n discrete grid, then the robber can forever evade ⌊n/2⌋ cops, but ⌊n/2⌋ + 1 cops can always capture the robber; they also proved tha... |

4 | Lion and man”: A postscript - Croft - 1964 |

4 |
and man: the general case
- Flynn, Lion
- 1974
(Show Context)
Citation Context ... that the man can move so as to avoid capture indefinitely. Variations have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], =-=[10]-=-, [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a ... |

3 |
The lion and man problem revisited
- Lewin
- 1986
(Show Context)
Citation Context ...Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin =-=[21]-=-, Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit by a robot [14]), the version we consider is more naturally described as a robber evadin... |

2 | Offline variants of the "Lion and Man" problem – Some problems and techniques for measuring crowdedness and for safe path planning –, Theoretical Computer Science 399(3
- Dumitrescu, Suzuki, et al.
- 2008
(Show Context)
Citation Context ...ps move adaptively, not on fixed routes.) In the continuous problem, the cops and the robber have the same maximum speed and move continuously in a continuous region. Dumitrescu, Suzuki, and Zylinski =-=[8]-=- asked, what is the maximum number of cops that a robber can evade on either an n × n discrete grid or on an n × n (continuous) square region? Among other results, they proved that Ω( √ n) cops can be... |

1 |
Lion and man: the boundary constraint
- Flynn
- 1973
(Show Context)
Citation Context ... show that the man can move so as to avoid capture indefinitely. Variations have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn =-=[9]-=-, [10], [11], Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit... |

1 |
Some results on max-min pursuit
- Flynn
- 1974
(Show Context)
Citation Context ...the man can move so as to avoid capture indefinitely. Variations have been studied by Alonso, Goldstein, and Reingold [2], Altshuler, Yanovsky, Wagner, and Bruckstein [3], Croft [7], Flynn [9], [10], =-=[11]-=-, Gale (see Guy [13]) and Sgall [28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a man by... |

1 |
The robot and the rabbit—a pursuit problem
- Halperin
- 1969
(Show Context)
Citation Context ...[28], Goldstein and Reingold [12], Isler, Kannan, and Khanna [16], Lewin [21], Merz [23], and Rote [27]. Although the problem is usually stated as a pursuit of a man by a lion (or a rabbit by a robot =-=[14]-=-), the version we consider is more naturally described as a robber evading cops on patrol. Specifically, we imagine that cops patrol a region on fixed routes and the robber has full knowledge of the c... |