[Paper Review] Hop Doubling Label Indexing for Point-to-Point Distance Querying on Scale-Free Networks

Minhao Jiang, Ada Wai-Chee Fu+2 more|arXiv (Cornell University)|Mar 4, 2014

Data Management and Algorithms27 references4 citations

TL;DR

This paper proposes Hop Doubling Label (HopDb) indexing, a disk-based method for efficient point-to-point distance querying in massive scale-free graphs. By leveraging hop-doubling and pruning strategies, it achieves small label sizes (under 200 entries per vertex) and scales to graphs with hundreds of millions of nodes, outperforming prior in-memory methods in indexing and query time.

ABSTRACT

We study the problem of point-to-point distance querying for massive scale-free graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a hop-doubling labeling technique. We derive bounds on the index size, the computation costs and I/O costs based on the properties of unweighted scale-free graphs. We show that our method is much more efficient compared to the state-of-the-art technique, in terms of both querying time and indexing time. Our empirical study shows that our method can handle graphs that are orders of magnitude larger than existing methods.

Motivation & Objective

• Address the scalability limitations of existing in-memory 2-hop labeling methods for large-scale-free graphs.
• Reduce index construction time and storage space while maintaining fast query performance.
• Enable indexing of graphs far larger than main memory by using a disk-based, iterative labeling approach.
• Guarantee small label sizes and bounded I/O and computation costs through properties of scale-free networks.
• Develop a method that supports efficient point-to-point distance queries on graphs with up to hundreds of millions of vertices.

Proposed method

• Use a novel iterative hop-doubling labeling process that grows candidate labels by doubling the hop count in each step.
• Introduce a hybrid strategy: use hop-stepping (limited growth) in early iterations to control label expansion, then switch to hop-doubling for acceleration.
• Apply pruning at each iteration to remove redundant or non-promising label entries, reducing candidate set size by up to 90%.
• Leverage the small hub dimension and small diameter properties of unweighted scale-free graphs to bound label size and iteration count.
• Construct the index in a bottom-up manner using a hierarchical decomposition, minimizing label growth while preserving shortest path semantics.
• Ensure disk-based I/O efficiency by minimizing random access and controlling intermediate data size through pruning and controlled growth.

Experimental results

Research questions

• RQ1 Can a disk-based indexing method achieve both small label size and low indexing time for massive scale-free graphs?
• RQ2 How does the combination of hop-doubling and hop-stepping with pruning affect label size and convergence speed?
• RQ3 To what extent do the structural properties of scale-free graphs (small diameter, small hub dimension) enable scalable indexing?
• RQ4 Can the proposed method handle graphs significantly larger than those supported by existing in-memory labeling techniques?
• RQ5 What is the trade-off between label size, indexing time, and query performance across diverse scale-free network topologies?

Key findings

• The average label size across all tested graphs remains below 200 entries per vertex, even for graphs with hundreds of millions of nodes.
• The method successfully indexes a 9GB graph using only 4GB of main memory, demonstrating strong scalability beyond main memory limits.
• For large graphs like wiki-English, the pruning strategy reduced candidate sets by up to 90% in later iterations, significantly improving efficiency.
• The hybrid approach (hop-stepping followed by hop-doubling) reduced indexing time by up to 50% compared to pure hop-doubling or hop-stepping alone.
• The number of iterations required for convergence decreased from 59 (hop-stepping only) to 15 (hybrid) on the wikiItaly graph, indicating faster convergence.
• The method achieved sub-second query times on large graphs, with label size remaining flat even as graph size increased linearly.