Cops and Robber with Constraints
نویسندگان
چکیده
Cops & Robber is a classical pursuit-evasion game on undirected graphs, where the task is to identify the minimum number of cops sufficient to catch the robber. In this paper, we investigate the changes in problem’s complexity and combinatorial properties with constraining the following natural game parameters • Fuel : The number of steps each cop can make; • Cost : The total sum of steps along edges all cops can make; • Time: The number of rounds of the game.
منابع مشابه
A cops and robber game in multidimensional grids
We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional grid, at least n cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber...
متن کاملOn Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids
We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional grid, at least n cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber...
متن کاملImproved bounds for cops-and-robber pursuit
We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than √ 5n and hence that bn/ √ 5c+ 1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869 · · ·n2 +O(n) cops can capture a robber in a n× n× n cube and that a robber can forev...
متن کاملCops and Robber Game in Multidimensional Grids
We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that in an n-dimensional grid, at least n cops are necessary if one wants to catch the robber under all possible initial configurations. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber.
متن کاملVariations of cops and robber on the hypercube
We determine the cop number of the hypercube for different versions of the game Cops and Robber. Cops and Robber is a two player game played on an undirected graph. One player controls some number of cops; the other player controls a single robber. In the standard game, the cops first choose some vertices to occupy, then the robber chooses a vertex; the players then alternate turns. On a turn, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 26 شماره
صفحات -
تاریخ انتشار 2012