Journal of information and communication convergence engineering

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Computing the Dominating-Free Set by Two Point Sets in the Plane

  • Kim, Soo-Hwan (Department of Embedded IT, Pusan University of Foreign Studies)
  • Received : 2011.01.10
  • Accepted : 2011.02.07
  • Published : 2011.01.01
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Abstract

In this paper, we study the dominating-free sest which is defined as follows: k points called servers and n points called clients in the plane are given. For a point p in the plane is said to be dominated by a client c if for every server s, the distance between s and p is greater than the distance between s and c. The dominating-free set is the set of points in the plane which aren't dominated by any client. We present an O(nklogk+$n^2k$) time algorithm for computing the dominating-free set under the $L_1$-metric. Specially, we present an O(nlogn) time algorithm for the problem when k=2. The algorithm uses some variables and 1-dimensional arrays as its principle data structures, so it is easy to implement and runs fast.

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References

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