2024/10/04 by Run Yan Teh, Teh, Run Yan, Manushan Thenabadu +3 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2410.03163
openalex publication_date 2024/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order is predicted for independent, factorable resources. We show that it equals the inverse sum of the inverse resource orders. This is applied to computing averages in a stochastic differential equation. We treat numerical examples for multiple different algorithms and for stochastic partial differential equations, all giving quantitative results in excellent agreement with our more general analytic theory.