New Additive Spanners
نویسنده
چکیده
This paper considers additive and purely additive spanners. We present a new purely additive spanner of size Õ(n) with additive stretch 4. This construction fills in the gap between the two existing constructions for purely additive spanners, one for 2-additive spanner of size O(n) and the other for 6-additive spanner of size O(n), and thus answers a main open question in this area. In addition, we present a construction for additive spanners with Õ(n) edges and additive stretch of Õ(n1/2−3δ/2) for any 3/17 6 δ < 1/3, improving the stretch of the existing constructions from O(n1−3δ) to Õ( √ n1−3δ). Finally, we show that our (1, n1/2−3δ/2)spanner construction can be tweaked to give a sublinear additive spanner of size Õ(n) with additive stretch O( √ distance).
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