Implementing Binary Search Trees in GP 2 (Extended Abstract)

TL;DR

This paper introduces a method to implement binary search trees in the rule-based graph language GP 2, achieving comparable theoretical time complexities to traditional implementations.

Contribution

It demonstrates how to implement binary search trees in GP 2 using graph transformation rules, with analysis of their efficiency and performance.

Findings

Operations have worst-case runtime of O(n).

Expected average runtime is O(log n).

Implementation matches imperative binary search tree performance.

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.