ShareDP: Finding k Disjoint Paths for Multiple Vertex Pairs

2025-02-23

AI Summary

This paper addresses the batch query problem of computing $k$ vertex-disjoint paths (kDP) for multiple source–sink vertex pairs, motivated by high-frequency concurrent applications such as network routing and traffic scheduling. To overcome the inefficiency of conventional per-query processing—characterized by redundant computation—and the poor scalability of brute-force enumeration, we propose the first shared-computation-based batch framework. Our approach unifies multiple queries via graph transformation and structured graph merging, designs a shared depth-first traversal algorithm, and integrates dynamic pruning with caching to reuse traversal states and intermediate results. Extensive experiments on 12 real-world datasets demonstrate that our method achieves up to 32× speedup over state-of-the-art approaches while reducing average memory consumption by 67%, significantly enhancing both efficiency and scalability for large-scale, dynamic batch kDP queries.

Technology Category

• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Finding k disjoint paths (kDP) is a fundamental problem in graph analysis. For vertices s and t, paths from s to t are said to be disjoint if any two of them share no common vertex except s and t. In practice, disjoint paths are widely applied in network routing and transportation. In these scenarios, multiple kDP queries are often issued simultaneously, necessitating efficient batch processing. This motivates the study of batch kDP query processing (batch-kDP). A straightforward approach to batch-kDP extends batch simple-path enumeration with disjointness checks. But this suffers from factorial computational complexity. An alternative approach leverages single-query algorithms that avoid this by replacing the graph with a converted version. However, handling each query independently misses opportunities for shared computation. To overcome these limitations, we propose ShareDP, an algorithm for batch-kDP that shares the computation and storage across kDPs. ShareDP merges converted graphs into a shared structure, then shares the traversals and operations from different queries within this structure. Extensive experiments on 12 real-world datasets confirm the superiority of ShareDP over comparative approaches.

Problem

• Efficient batch processing of k disjoint paths
• Shared computation across multiple kDP queries
• Overcoming factorial computational complexity in graph analysis

Innovation

• Batch kDP query processing
• Shared computation and storage
• Merged converted graph structure