2018

# A time–space trade-off for computing the k-visibility region of a point in a polygon

## Publication

### Publication

Let P be a simple polygon with n vertices, and let q∈P be a point in P. Let k∈{0,…,n−1}. A point p∈P is k-visible from q if and only if the line segment pq crosses the boundary of P at most k times. The k-visibility region of q in P is the set of all points that are k-visible from q. We study the problem of computing the k-visibility region in the limited workspace model, where the input resides in a random-access read-only memory of O(n) words, each with Ω(logn) bits. The algorithm can read and write O(s) additional words of workspace, where s∈N is a parameter of the model. The output is written to a write-only stream. Given a simple polygon P with n vertices and a point q∈P, we present an algorithm that reports the k-visibility region of q in P in O(cn/s+clogs+min{⌈k/s⌉n,nloglogsn}) expected time using O(s) words of workspace. Here, c∈{1,…,n} is the number of critical vertices of P for q where the k-visibility region of q may change. We generalize this result for polygons with holes and for sets of non-crossing line segments.

Additional Metadata | |
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k-Visibility region, Limited workspace model, Time–space trade-off | |

dx.doi.org/10.1016/j.tcs.2018.06.017 | |

Theoretical Computer Science | |

Organisation | School of Computer Science |

Bahoo, Y. (Yeganeh), Banyassady, B. (Bahareh), Bose, P, Durocher, S. (Stephane), & Mulzer, W. (Wolfgang). (2018). A time–space trade-off for computing the k-visibility region of a point in a polygon.
Theoretical Computer Science. doi:10.1016/j.tcs.2018.06.017 |