Cache-Oblivious Polygon Indecomposability Testing

摘要

We examine a cache-oblivious reformulation of the (iterative) polygon indecomposability test of [19]. We analyse the cache complexity of the iterative version of this test within the ideal-cache model and identify the bottlenecks affecting its memory performance. Our analysis reveals that the iterative algorithm does not address data locality and that memory accesses progress with arbitrarily sized jumps in the address space. We reformulate the iterative computations of [19] according to a DFS traversal of the computation tree and obtain, as a result, a cache-oblivious variant which exhibits asymptotically improved spatial and temporal locality over the original one. In particular, we show that the DFS variant ensures spatial locality, and describe quantitatively the asymptotic improvements in spatial and temporal locality. In an extension to this work appearing in [3], the DFS variant is implemented in relation to absolute irreducibility of bivariate polynomials over arbitrary fields, and tested against both the original version as given in [19] and the powerful computer algebra system MAGMA. The results demonstrate significantly improved performance for the DFS variant as indicated by LI misses, L2 misses, and total execution time.