[Paper Review] A Highly Scalable Labelling Approach for Exact Distance Queries in Complex Networks

Muhammad Farhan, Qing Wang+2 more|arXiv (Cornell University)|Dec 6, 2018

Graph Theory and Algorithms32 references4 citations

TL;DR

This paper presents a highly scalable labeling approach for exact distance queries in billion-scale complex networks, combining a novel highway cover distance labeling algorithm with distance-bounded search on sparsified graphs. It achieves up to 70× faster labeling construction and 90% space reduction while answering queries in under 1ms on 8B-edge networks, enabling practical exact distance computation at unprecedented scale.

ABSTRACT

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 techniques to efficiently construct distance labelling and process exact shortest path distance queries for complex networks with billions of vertices and billions of edges. Our method is based on two ingredients: (i) a scalable labelling algorithm for constructing minimal distance labelling, and (ii) a querying framework that supports fast distance-bounded search on a sparsified graph. Thus, we first develop a novel labelling algorithm that can scale to graphs at the billion-scale. Then, we formalize a querying framework for exact distance queries, which combines our proposed highway cover distance labelling with distance-bounded searches to enable fast distance computation. To speed up the labelling construction process, we further propose a parallel labelling method that can construct labelling simultaneously for multiple landmarks. We evaluated the performance of the proposed methods on 12 real-world networks. The experiments show that the proposed methods can not only handle networks with billions of vertices, but also be up to 70 times faster in constructing labelling and save up to 90\% of labelling space. In particular, our method can answer distance queries on a billion-scale network of around 8B edges in less than 1ms, on average.

Motivation & Objective

• Address the lack of scalable solutions for exact shortest-path distance queries in billion-scale complex networks.
• Overcome the quadratic space and prohibitively long preprocessing times of existing labeling methods on large graphs.
• Develop a labeling algorithm that scales linearly with the number of landmarks and minimizes label size.
• Enable fast, constant-time query responses (under 1ms) even on networks with billions of vertices and edges.
• Design a parallelizable framework to accelerate labeling construction across multiple landmarks.

Proposed method

• Propose a novel highway cover distance labeling (HWC) algorithm that constructs minimal, ordering-independent labels for exact distance queries.
• Introduce a distance-bounded search framework that operates on a sparsified graph to accelerate query processing.
• Use spanning trees as highways to guide efficient 2-hop labeling construction, preserving distance accuracy.
• Develop a parallel BFS-based labeling method that simultaneously processes multiple landmarks, significantly reducing preprocessing time.
• Formalize a querying mechanism that combines HWC labeling with bounded-search to compute exact distances rapidly.
• Apply graph sparsification to reduce the search space during queries without sacrificing accuracy.

Experimental results

Research questions

• RQ1 Can a labeling-based method scale to billion-scale networks while maintaining minimal label size and fast query times?
• RQ2 How can the construction time of distance labeling be reduced for large graphs without compromising label minimality?
• RQ3 What is the impact of landmark ordering and selection on label size and query performance in large-scale networks?
• RQ4 Can parallelization of BFS computations over multiple landmarks significantly accelerate labeling construction?
• RQ5 To what extent can graph sparsification and bounded-search techniques improve query efficiency in large networks?

Key findings

• The proposed method constructs labels up to 70 times faster than state-of-the-art methods on billion-scale networks.
• Labeling space is reduced by up to 90% compared to existing approaches, enabling deployment on memory-constrained systems.
• Distance queries on an 8-billion-edge network are answered in less than 1ms on average, achieving sub-millisecond response times.
• The labeling algorithm produces HWC-minimal labels that are independent of landmark ordering, ensuring optimal label size.
• The parallel labeling framework enables scalable, linear-time construction proportional to the number of landmarks, making it feasible for billion-scale graphs.
• The method outperforms prior works such as FD (Hayashi et al., 2016) and PLL (Akiba et al., 2013) in both construction time and space efficiency on large networks.