Optimizing Time Complexity: A Comparative Analysis of Techniques in Recursive Algorithms - A Case Study with Path Sum Algorithm in Graphs and Binary Trees

11 pages•Published: March 21, 2024

Abstract

Programming infrastructures commonly employ graphs and binary trees to model systems and networks. Efficient operations on trees and graphs are pivotal in enhancing software performance and reducing computational costs, particularly for data-dependent tasks during runtime. This paper analyzes the optimization techniques for recursive algorithms, focusing on the widely used Path Sum algorithm designed for identifying cumulative value sequences that equal a specified target. Employing three distinct techniques—recursion, tabulation, and memoization—this study evaluates their computation time on two prominent data structures: trees and graphs. Results indicate that the memoization approach is completed in less computational time than the regular approach. In contrast, the tabular approach completes in significantly increased computational time, suggesting its inadequacy for traversal optimization. The findings affirm that optimization techniques, particularly memoization, effectively reduce traversal computation time, offering valuable insights for educators and developers working with recursive algorithms in graph and tree-based systems.

Keyphrases: binary tree, graph, memoization, Optimization, recursion, Tabulation

In: Ajay Bandi, Mohammad Hossain and Ying Jin (editors). Proceedings of 39th International Conference on Computers and Their Applications, vol 98, pages 129--139

Links:	https://easychair.org/publications/paper/MSbn
	https://doi.org/10.29007/8p9v