Teramoto et al. [22] defined a new measure called the gap ratio that measures the uniformity of a finite point set sampled from S, a bounded subset of ∝ 2. We attempt to generalize the definition of this measure over all metric spaces. We solve optimization related questions about selecting uniform point samples from metric spaces; the uniformity is measured using gap ratio. We give lower bounds for specific metric spaces, prove hardness and approximation hardness results. We also give a general approximation algorithm framework giving different approximation ratios for different metric spaces and give a (1 +ϵ)-approximation algorithm for a set of points in a Euclidean space.
CITATION STYLE
Bishnu, A., Desai, S., Ghosh, A., Goswami, M., & Paul, S. (2015). Uniformity of point samples in metric spaces using gap ratio. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9076, pp. 347–358). Springer Verlag. https://doi.org/10.1007/978-3-319-17142-5_30
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