A Relational Theory of Locality

Abstract

In many areas of program and system analysis and optimization, locality is a common concept and has been defined and measured in many ways. This article aims to formally establish relations between these previously disparate types of locality. It categorizes locality definitions in three groups and shows whether and how they can be interconverted. For the footprint, a recent metric, it gives a new measurement algorithm that is asymptotically more time/space efficient than previous approaches. Using the conversion relations, the new algorithm derives with the same efficiency different locality metrics developed and used in program analysis, memory management, and cache design.