Related papers: On the Complexity of Hub Labeling

Hub Labeling (HL) is one of the state-of-the-art preprocessing-based techniques for route planning in road networks. It is a special incarnation of distance labeling, and it is well-studied in both theory and practice. The core concept of…

In the context of distance oracles, a labeling algorithm computes vertex labels during preprocessing. An $s,t$ query computes the corresponding distance from the labels of $s$ and $t$ only, without looking at the input graph. Hub labels is…

There has been significant success in designing highly efficient algorithms for distance and shortest-path queries in recent years; many of the state-of-the-art algorithms use the hub labeling framework. In this paper, we study the…

Distance labeling is a preprocessing technique introduced by Peleg [Journal of Graph Theory, 33(3)] to speed up distance queries in large networks. Herein, each vertex receives a (short) label and, the distance between two vertices can be…

A reachability oracle (or hop labeling) assigns each vertex v two sets of vertices: Lout(v) and Lin(v), such that u reaches v iff Lout(u) \cap Lin(v) \neq \emptyset. Despite their simplicity and elegance, reachability oracles have failed to…

Answering the shortest-path distance between two arbitrary locations is a fundamental problem in road networks. Labelling-based solutions are the current state-of-the-arts to render fast response time, which can generally be categorised…

Computing the shortest-path distance between any two given vertices in road networks is an important problem. A tremendous amount of research has been conducted to address this problem, most of which are limited to static road networks.…

Finding a cycle of lowest weight that represents a homology class in a simplicial complex is known as homology localization (HL). Here we address this NP-complete problem using parameterized complexity theory. We show that it is W[1]-hard…

A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. An important class of distance…

A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. We propose a series of new labeling…

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

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…

Traditionally, classifying large hierarchical labels with more than 10000 distinct traces can only be achieved with flatten labels. Although flatten labels is feasible, it misses the hierarchical information in the labels. Hierarchical…

Recent works on Hierarchical Clustering (HC), a well-studied problem in exploratory data analysis, have focused on optimizing various objective functions for this problem under arbitrary similarity measures. In this paper we take the first…

Many real-world applications operate on dynamic graphs that undergo rapid changes in their topological structure over time. However, it is challenging to design dynamic algorithms that are capable of supporting such graph changes…

Recently, hashing methods have been widely used in large-scale image retrieval. However, most existing hashing methods did not consider the hierarchical relation of labels, which means that they ignored the rich information stored in the…

Hierarchical multi-label classification (HMLC) is essential for modeling complex label dependencies in remote sensing. Existing methods, however, struggle with multi-path hierarchies where instances belong to multiple branches, and they…

Large Language Models (LLMs) are increasingly deployed across diverse domains, raising the need for rigorous reliability assessment methods. Existing benchmark-based evaluations primarily offer descriptive statistics of model accuracy over…

Assigning a set of labels to a given text is a classification problem with many real-world applications, such as recommender systems. Two separate research streams address this issue. Hierarchical Text Classification (HTC) focuses on…

Data similarity (or distance) computation is a fundamental research topic which fosters a variety of similarity-based machine learning and data mining applications. In big data analytics, it is impractical to compute the exact similarity of…