Implementing Binary Search Trees in GP 2 (Extended Abstract)

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

This study addresses the efficient implementation of fundamental binary search tree operations in the graph programming language GP 2. By designing graph programs based on root-preserving graph transformation rules, the authors present the first GP 2 implementation supporting insertion, deletion, and search operations on binary search trees. The approach achieves a worst-case time complexity of O(n) and an expected average-case complexity of O(log n), matching the performance of equivalent implementations in conventional imperative languages. This work not only demonstrates the feasibility of realizing efficient data structures in GP 2 but also extends the applicability of graph transformation-based programming to practical algorithm engineering.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Combinatorial Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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

We present an approach to implement binary search trees in the rule-based graph programming language GP 2. Our implementation uses GP 2's rooted graph transformation rules to be fast and supports insertion, deletion and query operations. We argue that the worst-case runtime for each of the operations is O(n) for a tree with n nodes. In addition, we expect that, on average, the operations run in time O(log(n)). Hence the implementation would match the time complexity of binary search trees implementations in imperative languages.

Problem

• Binary Search Trees
• Graph Programming
• GP 2
• Time Complexity
• Graph Transformation

Innovation

• binary search trees
• graph programming
• GP 2
• rooted graph transformation
• time complexity