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.

Improving the performance of bagging ensembles for data streams through mini-batching

“…To date, this is the first work to propose a strategy for improving memory access locality for parallel implementation of bagging ensembles on multi-core systems. Our work employs [6] Increase the utilization of resources Web search engines Carbone et al [7] Fault tolerance and performance Apache Flink Gaioso et al [13] Increase the utilization of resources Web search engines He et al [19] Reduce recomputing and IO redundancies Large-scale data streams Kukreja et al [26] Reduce data movement Large-scale FWI Wang et al [42] Energy optimization Real-time tasks on heterogeneous sensors Wen et al [45] Reduce data on weight matrix ANNs for image classification Zaharia et al [49] Fault tolerance and performance Apache Spark Zhang et al [50] Reduce delay and energy consumption DNNs on the edge both measurement techniques and theoretical foundations proposed in [48] to demonstrate the benefits of mini-batching for the implementation of ensembles. The present work is different from previous work as we focus on a class of ensemble algorithms composed of bagging ensembles executing in the context of data streams.…”

“…Memory locality is a fundamental property and design principle for optimizing the performance of hardware, software, and algorithms [48]. Locality can be defined as "the tendency for programs to cluster references to subsets of address space for extended periods" [10].…”

“…Due to the increasing gap in processor and memory speeds [24], the locality has played a central role in optimizing the performance of operating systems over the decades. Locality may be defined in many ways, and several metrics related to it have been proposed [48]. We can use the notion of reuse distance (RD) to evaluate how mini-batching can improve the performance and resource (i.e., cache) sharing of bagging ensembles implementations.…”

“…We can use the notion of reuse distance (RD) to evaluate how mini-batching can improve the performance and resource (i.e., cache) sharing of bagging ensembles implementations. We chose these definitions because they are based on direct measurements, do not depend on idealistic assumptions, and are extensions of observational stochastic [48]. Our goal is to reduce cache misses by improving data reuse in parallel implementations of ensembles.…”

“…From a historical perspective, memory locality has been studied over decades to optimize the memory hierarchy, operating systems, software, and algorithms design with recent advances in measurement techniques [23], trace generation [40], and formal modeling [29]. In recent work [48], Yuan et al built upon previous works by proposing the relational theory of locality (RTL), a theoretical framework that unifies several memory locality measures used along five decades of study and research in the field. RTL provides mathematical background and categorizes the measures in three different types of locality.…”