Lion and Man with Visibility in Monotone Polygons

نویسندگان

  • Narges Noori
  • Volkan Isler
چکیده

In the original version of the lion and man game, a lion tries to capture a man who is trying to escape in a circular arena. The players have equal speeds. They can observe each other at all times. We study a new variant of the game in which the lion has only line-of-sight visibility. That is it can observe the man’s position only if the line segment connecting them does not intersect the boundary. We show that despite this limitation, the lion can capture the man in any monotone polygon in finite time.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the VC-Dimension of Visibility in Monotone Polygons

We show that the VC-dimension of visibility on the boundary of a monotone polygon is exactly 6. Our lower bound construction matches the best known lower bound for simple polygons.

متن کامل

Single-Point Visibility Constraint Minimum Link Paths in Simple Polygons

We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path. The method is based on partitioning a portion of $P$ into a number of faces of equal link distance from a source point. This partitioning is essentially a shor...

متن کامل

Line-of-Sight Pursuit in Strictly Sweepable Polygons

We study a turn-based game in a simply connected polygonal environmentQ between a pursuer P and an adversarial evader E . Both players can move in a straight line to any point within unit distance during their turn. The pursuer P wins by capturing the evader, meaning that their distance satisfies d(P, E) ≤ 1, while the evader wins by eluding capture forever. Both players have a map of the envir...

متن کامل

Convexifying Monotone Polygons while Maintaining Internal Visibility

Let P be a simple polygon on the plane. Two vertices of P are visible if the open line segment joining them is contained in the interior of P . In this paper we study the following questions posed in [5, 6]: (1) Is it true that every non-convex simple polygon has a vertex that can be continuously moved such that during the process no vertex-vertex visibility is lost and some vertex-vertex visib...

متن کامل

Generating Random Polygons with Given Vertices

The problem of generating \random" geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the speciic problem of generating a random x-monotone polygon on a given set of n vertices. Here, \random" is taken to mean that we select uniformly at random a polygon, from among all those x-monotone polygons having the given n vertices. We give an algo...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012