Beyond Highway Dimension: Small Distance Labels Using Tree Skeletons

Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond

For fixed $h \geq 2$, we consider the task of adding to a graph $G$ a set of weighted shortcut edges on the same vertex set, such that the length of a shortest $h$-hop path between any pair of vertices in the augmented graph is exactly the same as the original distance between these vertices in $G$. A set of shortcut edges with this property is called an exact $h$-hopset and may be applied in processing distance queries on graph $G$. In particular, a $2$-hopset directly corresponds to a distributed distance oracle known as a hub labeling. In this work, we explore centralized distance oracles b…

On the Complexity of Hub Labeling

Hub Labeling (HL) is a data structure for distance oracles. Hierarchical HL (HHL) is a special type of HL, that received a lot of attention from a practical point of view. However, theoretical questions such as NP-hardness and approximation guarantee for HHL algorithms have been left aside. In this paper we study HL and HHL from the complexity theory point of view. We prove that both HL and HHL are NP-hard, and present upper and lower bounds for the approximation ratios of greedy HHL algorithms used in practice. We also introduce a new variant of the greedy HHL algorithm and a proof that it pr…

Hierarchical Cut Labelling——扩展道路网络上距离查询的规模

Hierarchical Cut Labelling -- Scaling Up Distance Queries on Road Networks

针对道路网络最短路径距离查询中标记大小和搜索空间难以兼顾的问题，提出结合层次结构优势的 HC2L 方法，通过 balanced tree hierarchy 减小标记并加速查询，同时提供并行变体 HC2L$^p$，在 10 个大型真实路网上验证了有效性。

A Highly Scalable Labelling Approach for Exact Distance Queries in Complex Networks

Answering exact shortest path distance queries is a fundamental task in graph theory. Despite a tremendous amount of research on the subject, there is still no satisfactory solution that can scale to billion-scale complex networks. Labelling-based methods are well-known for rendering fast response time to distance queries; however, existing works can only construct labelling on moderately large networks (million-scale) and cannot scale to large networks (billion-scale) due to their prohibitively large space requirements and very long preprocessing time. In this work, we present novel technique…

Shortest path queries, graph partitioning and covering problems in worst and beyond worst case settings

In this thesis, we design algorithms for several NP-hard problems in both worst and beyond worst case settings. In the first part of the thesis, we apply the traditional worst case methodology and design approximation algorithms for the Hub Labeling problem; Hub Labeling is a preprocessing technique introduced to speed up shortest path queries. Before this work, Hub Labeling had been extensively studied mainly in the beyond worst case analysis setting, and in particular on graphs with low highway dimension. In this work, we significantly improve our theoretical understanding of the problem and…