Abstract
Motivated by the recent trend of increasing number of e-cars and hybrid cars, we investigate the problem of building a red-black spanner for a mixed-charging vehicular network. In such a network, we have two kinds of gas/charging stations: electric (black) and the traditional gas (red) stations. Our requirement is that one cannot connect two gas stations directly in the spanner (i.e., no red-red edge), and our goal is to build a linear-size spanner with a bounded stretch factor under this requirement. (In 2-d, it can be shown that a spanner with an optimal stretch factor could have a quadratic size and if one is restricted to build the spanner purely from a given road network then it is impossible to obtain a bounded stretch factor.) Our main results are summarized as follows.
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1.
In 1-d, we show a linear-size red-black spanner satisfying the ‘no red-red edge’ requirement which achieves the optimal stretch factor.
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2.
In 2-d and under the \(L_2\) metric, we show a linear-size red-black spanner satisfying the ‘no red-red edge’ requirement which achieves a stretch factor of 1.998.
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3.
In 2-d and under the \(L_1\) metric, we show a linear-size red-black spanner satisfying the ‘no red-red edge’ requirement which achieves a stretch factor of 3.613.
This work is partially supported by JSPS KAKENHI Grant Number 19H04068.
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Part of this research was done while the first and last author visited University of Hyogo in late 2022.
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Bereg, S., Higashikawa, Y., Katoh, N., Teruyama, J., Tokuni, Y., Zhu, B. (2024). Red-Black Spanners for Mixed-Charging Vehicular Networks. In: Wu, W., Tong, G. (eds) Computing and Combinatorics. COCOON 2023. Lecture Notes in Computer Science, vol 14422. Springer, Cham. https://doi.org/10.1007/978-3-031-49190-0_16
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