A new bound for map labeling with uniform circle pairs
نویسندگان
چکیده
Given a planar point set, we wish to label the points with uniform circular labels such that each input point lies on the boundary of two labels, none of the interiors of the labels intersect, and the size of the labels is maximized. This problem is known as map-labeling with uniform circular pairs (MLUCP) and has been shown to be NP-hard. In this paper, we give an O(n logn) time, O(n) space algorithm that computes a labeling, such that the diameter of the circular labels in an optimum solution is no more than (1 +√33)/4 ≈ 1.686 times the diameter of the labels computed by our algorithm. 2002 Elsevier Science B.V. All rights reserved.
منابع مشابه
New Bounds on Map Labeling with Circular Labels
We present new approximation algorithms for the NP-hard problems of labeling points with maximum-size uniform circles and circle pairs (MLUC and MLUCP). Our algorithms build on the important concept of maximal feasible region and new algorithmic techniques. We obtain several results: a (2.98 + )-approximation for MLUC, improving previous factor 3.0+ ; a (1.491+ )-approximation for MLUCP, improv...
متن کاملMap Labeling with Circles
We study two geometric optimization problems motivated by cartographic applications: Map Labeling with Uniform Circles (MLUC) and Map Labeling with Uniform Circle Pairs (MLUCP). We show that the decision problems of both MLUC and MLUCP are NP-hard, and that the related optimization problems for maximizing the label sizes are NP-hard to approximate within factor 1.0349. We design approximation a...
متن کامل3-difference cordial labeling of some cycle related graphs
Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...
متن کامل$Z_k$-Magic Labeling of Some Families of Graphs
For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-textit{magic} if there exists a labeling $f:E(G) rightarrow A-{0}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k...
متن کاملNew Phases of Near-Extremal Branes on a Circle
We study the phases of near-extremal branes on a circle, by which we mean near-extremal branes of string theory and M-theory with a circle in their transverse space. We find a map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle Md×S1, and map it to a corresponding solution for a near-extremal brane on a circle. ...
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:
- Inf. Process. Lett.
دوره 81 شماره
صفحات -
تاریخ انتشار 2002