Abstract
In this paper, we consider two new variants of the unit covering problem in color-spanning set model: Given a set of n points in d-dimensional plane colored with m colors, the MinCSBC problem is to select m points of different colors minimizing the minimum number of unit balls needed to cover them. Similarly, the MaxCSBC problem is to choose one point of each color to maximize the minimum number of needed unit balls. We show that MinCSBC is NP-hard and hard to approximate within any constant factor even in one dimension. For d = 1, however, we propose an ln (m)-approximation algorithm and present a constant-factor approximation algorithm for fixed f, where f is the maximum frequency of the colors. For the MaxCSBC problem, we first prove its NP-hardness. Then we present an approximation algorithm with a factor of 1/2 in one-dimensional case.
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Emamjomeh-Zadeh, E., Ghodsi, M., Homapour, H., Seddighin, M. (2015). Unit Covering in Color-Spanning Set Model. In: Rahman, M.S., Tomita, E. (eds) WALCOM: Algorithms and Computation. WALCOM 2015. Lecture Notes in Computer Science, vol 8973. Springer, Cham. https://doi.org/10.1007/978-3-319-15612-5_5
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DOI: https://doi.org/10.1007/978-3-319-15612-5_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-15611-8
Online ISBN: 978-3-319-15612-5
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