Verification Challenge: Fractional Cascading for Multi-Nuclide Grid Lookup

TL;DR

The paper addresses verifying a fractional cascading-based cascade grid for multi-nuclide energy-grid lookup in nuclear cross section interpolation. It outlines a cascade-grid construction with augmented grids $M_1,\dots,M_k$ and per-entry indices $p_1, p_2$, enabling a single initial binary search followed by constant-time refinements to obtain all $k$ lookups. It proves a correctness claim and a structural bound on size, and provides a C implementation with a guidance for full verification against naive $k$ binary searches. The work aims to enable fast, scalable cross-section lookups in particle transport simulations by reducing per-query cost while preserving exact results.

Abstract

We present a verification challenge based on the fractional cascading (FC) technique for accelerating repeated searches across a collection of sorted arrays. The specific context is nuclear cross section lookup in a simulation code, where a material consists of many nuclides, each with its own sorted energy grid. A naive search performs a binary search in each array individually. The FC-based cascade grid structure reduces this cost by performing a single binary search followed by constant-time refinements. The challenge consists of verifying the correctness of the FC algorithm with respect to the naive approach and validating its structural properties.