Multi-level Weighted Additive Spanners ∗
Multi-level Weighted Additive Spanners ∗
复制标题
多级加权附加扳手*
DOI：
10.4230/lipics.sea.2021.16
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Spence
中科院分区：
文献类型：
--
作者：
R. Ahmed;Gregory Bodwin;Faryad Darabi;Keaton Hamm;Stephen G. Kobourov;Richard Spence;Keaton Sahneh;Stephen Hamm;Kobourov Richard;Spence
给定图G =（v，e），如果disth（u，v）≤distg（u，v） +β对于所有u，v∈V在输入上给出的特定c对P⊆v×v必须仅保留上述不等式的扳手，并且当对具有某些子集S v的结构p = s×s时，它被特别称为子集扳手。在未加权的图在文献中进行了广泛的研究，但直到最近才被推广到加权图。或服务质量（QoS）要求，目标是计算最小边数的嵌套序列。 [Pettie 2008，Cygan等人，2013年]到加权设置。多级问题。由几个不同的随机图生成器生成的输入图：erdős
Given a graph G = ( V, E ), a subgraph H is an additive + β spanner if dist H ( u, v ) ≤ dist G ( u, v ) + β for all u, v ∈ V . A pairwise spanner is a spanner for which the above inequality only must hold for specific pairs P ⊆ V × V given on input, and when the pairs have the structure P = S × S for some subset S ⊆ V , it is specifically called a subsetwise spanner. Spanners in unweighted graphs have been studied extensively in the literature, but have only recently been generalized to weighted graphs. In this paper, we consider a multi-level version of the subsetwise spanner in weighted graphs, where the vertices in S possess varying level, priority, or quality of service (QoS) requirements, and the goal is to compute a nested sequence of spanners with the minimum total number of edges. We first generalize the +2 subsetwise spanner of [Pettie 2008, Cygan et al., 2013] to the weighted setting. We experimentally measure the performance of this and several other algorithms for weighted additive spanners, both in terms of runtime and sparsity of output spanner, when applied at each level of the multi-level problem. Spanner sparsity is compared to the sparsest possible spanner satisfying the given error budget, obtained using an integer programming formulation of the problem. We run our experiments with respect to input graphs generated by several different random graph generators: Erdős
更好的距离保持器和附加扳手
影响因子：
1.3
作者：
Bodwin, Greg;Williams, Virginia Vassilevska
通讯作者：
Williams, Virginia Vassilevska
加权附加扳手
DOI：
10.1007/978-3-030-60440-0_32
发表时间：
2020
期刊：
46th International Workshop on Graph-Theoretic Concepts in Computer Science (WG
影响因子：
--
作者：
Ahmed, R;Bodwin, G;Darabi, F;Kobourov, S;Spence, R
通讯作者：
Spence, R
基于Kruskal的多级Steiner树问题逼近算法
DOI：
--
发表时间：
2020
期刊：
28th Annual European Symposium on Algorithms (ESA
影响因子：
--
作者：
Ahmed, R;Darabi, F;Hamm, K;Kobourov, S;Spence, R.
通讯作者：
Spence, R.