Random Rank-Based, Hierarchical or Trivial: Which Dynamic Graph Algorithm Performs Best in Practice?

On Dasgupta's hierarchical clustering objective and its relation to other graph parameters

The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees. Motivated by a correspondence with Dasgupta's objective for hierarchical clustering we consider the total rather than maximum depth of vertices as an alternative objective for minimization. For vertex partition trees this leads to a new parameter with a natural interpretation as a measure of robustness against vertex removal. As tools for the study of this family of…

Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean closest pairs, we show how to insert and delete objects from an n-object set, maintaining the closest pair, in O(n log^2 n) time per update and O(n) space. With quadratic space, we can instead use a quadtree-like structure to achieve an optimal time bound, O(n) per update. We apply these data structures to hierarchical clustering, greedy matching, and TSP heurist…

HENN：一种用于近似最近邻搜索的层次化ε-网导航图

HENN: A Hierarchical Epsilon Net Navigation Graph for Approximate Nearest Neighbor Search

提出层次化ε-网导航图HENN，结合理论保证与实践效率，实现多对数查询时间并保持高召回率，在多种数据分布下优于现有方法。

Fully-dynamic Weighted Matching Approximation in Practice

Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is based on random walks/paths combined with dynamic programming. The second algorithm has been introduced by Stubbs and Williams without an implementation. Roughly speaking, their algorithm uses dynamic unweighted matching algorithms as a subroutine (within a multilevel approach); this allows us to use previous work on dynamic unweighted matching algorithms as…

一种用于多车辆电话叫车问题的分层分组算法

A Hierarchical Grouping Algorithm for the Multi-Vehicle Dial-a-Ride Problem

针对多车辆 DaRP，本文提出首个非平凡近似算法 HRA，通过归约为带容量划分问题并采用分层分组求解，实验显示其路线更短且在途延迟更小。

Hierarchical Categories in Colored Searching

In colored range counting (CRC), the input is a set of points where each point is assigned a ``color'' (or a ``category'') and the goal is to store them in a data structure such that the number of distinct categories inside a given query range can be counted efficiently. CRC has strong motivations as it allows data structure to deal with categorical data. However, colors (i.e., the categories) in the CRC problem do not have any internal structure, whereas this is not the case for many datasets in practice where hierarchical categories exists or where a single input belongs to multiple categori…