• Journal of the Korean Association of Geographic Information Studies
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• v.22 no.4
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• pp.169-180
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• 2019

Shorelines should be extracted with consistency because they are the reference for determining the shape of a country. Even in the same area, inconsistent minimum vertex intervals cause inconsistencies in the coastline length, making it difficult to acquire reliable primary data for national policy decisions. As the shoreline length cannot be calculated consistently for shorelines produced by determining the arbitrary distance between points below 1m, a methodology to calculate consistent shoreline length using the minimum vertex interval is proposed herein. To compare our results with the shoreline length published by KHOA(Korea Hydrographic and Oceanographic Agency) and analyze the change in shoreline length according to the minimum vertex interval, target sites was selected and the grid overlap of the shoreline was determined. Based on the comparison results, minimum grid sizes and the minimum vertex interval can be determined by deriving a polynomial function that estimates minimum grid sizes for determining consistent shoreline lengths. By comparing public shoreline lengths with generalized shoreline lengths using various grid sizes and by analyzing the characteristics of the shoreline according to vertex intervals, the minimum vertex intervals required to achieve consistent shoreline lengths could be estimated. We suggest that the minimum vertex interval methodology by quantitative evaluation of the determined grid size may be useful in calculating consistent shoreline lengths. The proposed method by minimum vertex interval determination can help derive consistent shoreline lengths and increase the reliability of national shorelines.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.1-11
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• 2010

The conditional covering problem is an important variation of well studied set covering problem. In the set covering problem, the problem is to find a minimum cardinality vertex set which will cover all the given demand points. The conditional covering problem asks to find a minimum cardinality vertex set that will cover not only the given demand points but also one another. This problem is NP-complete for general graphs. In this paper, we present an efficient algorithm to solve the conditional covering problem on interval graphs with n vertices which runs in O(n)time.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.11
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• pp.2103-2108
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• 2017

For n points $p_i$ on the m-dimensional plane $R^m$ and a fixed range r, consider a set $T_i$ containing points the distances from $p_i$ of which are less than or equal to r. In case m=1, $T_i$ is an interval on a line, it is a circle on a plane when m=2. For the vertices corresponding to the sets $T_i$, there is an edge between the vertices if the two sets intersect. Then this graph is called an intersection graph G. For m=1 G is called a proper interval graph and for m=2, it is called an unit disk graph. In this paper, we are concerned in the intersection graph G(r) when r changes. In particular, we consider the problem to find the minimum r such that G(r)is connected. For this problem, we propose an O(n) algorithm for the proper interval graph and an $O(n^2{\log}\;n)$ algorithm for the unit disk graph. For the dynamic environment in which the points on a line are added or deleted, we give an O(log n) algorithm for the problem.