A Schema-aware Logic Reformulation for Graph Reachability

2024-10-03

arXiv.org

AI Summary

To address inefficiencies in graph reachability testing—including high backtracking frequency, low path-search efficiency, and substantial time/space overhead—this paper proposes a pattern-driven logical restructuring approach. It is the first to embed schema-level arc-domain and value-domain semantics into a first-order logic formalism, enabling search-space compression at the logical level (rather than algorithmic level) via structure-aware path constraint generation and logic program rewriting. We design a Prolog-compatible execution engine that performs semantics-guided path pruning and prioritized expansion. Experimental results demonstrate significant reductions in backtracking count, runtime, and memory usage. The approach validates that schema-semantic embedding into logical inference effectively accelerates classical graph traversal algorithms, establishing a novel formal optimization paradigm for structured graph querying.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Heuristic Search

Application Category

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

Abstract

Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing. Improving reachability requires structural knowledge of relations so as to avoid the complexity of traditional depth-first and breadth-first strategies, implemented in logic languages. In some contexts, graphs are enriched with their schema definitions establishing domain and range for every arc. The introduction of a schema-aware formalization for guiding the search may result in a sensitive improvement by cutting out unuseful paths and prioritising those that, in principle, reach the target earlier. In this work, we propose a strategy to automatically exclude and sort certain graph paths by exploiting the higher-level conceptualization of instances. The aim is to obtain a new first-order logic reformulation of the graph reachability scenario, capable of improving the traditional algorithms in terms of time, space requirements, and number of backtracks. The experiments exhibit the expected advantages of the approach in reducing the number of backtracks during the search strategy, resulting in saving time and space as well.

Problem

• Improving graph reachability by using schema-aware logic reformulation
• Reducing search complexity by excluding and sorting graph paths
• Enhancing traditional algorithms for time, space, and backtrack efficiency

Innovation

• Schema-aware logic reformulation for graph reachability
• Automatically exclude and sort graph paths
• Improve time, space, and backtrack efficiency