Efficient parameterized algorithms for data packing

There is a huge gap between the speeds of modern caches and main memories, and therefore cache misses account for a considerable loss of efficiency in programs. The predominant technique to address this issue has been Data Packing: data elements that are frequently accessed within time proximity are packed into the same cache block, thereby minimizing accesses to the main memory. We consider the algorithmic problem of Data Packing on a two-level memory system. Given a reference sequence R of accesses to data elements, the task is to partition the elements into cache blocks such that the number of cache misses on R is minimized. The problem is notoriously difficult: it is NP-hard even when the cache has size 1, and is hard to approximate for any cache size larger than 4. Therefore, all existing techniques for Data Packing are based on heuristics and lack theoretical guarantees. In this work, we present the first positive theoretical results for Data Packing, along with new and stronger negative results. We consider the problem under the lens of the underlying access hypergraphs, which are hypergraphs of affinities between the data elements, where the order of an access hypergraph corresponds to the size of the affinity group. We study the problem parameterized by the treewidth of access hypergraphs, which is a standard notion in graph theory to measure the closeness of a graph to a tree. Our main results are as follows: We show there is a number q* depending on the cache parameters such that (a) if the access hypergraph of order q* has constant treewidth, then there is a linear-time algorithm for Data Packing; (b)the Data Packing problem remains NP-hard even if the access hypergraph of order q*-1 has constant treewidth. Thus, we establish a fine-grained dichotomy depending on a single parameter, namely, the highest order among access hypegraphs that have constant treewidth; and establish the optimal value q* of this parameter. Finally, we present an experimental evaluation of a prototype implementation of our algorithm. Our results demonstrate that, in practice, access hypergraphs of many commonly-used algorithms have small treewidth. We compare our approach with several state-of-the-art heuristic-based algorithms and show that our algorithm leads to significantly fewer cache-misses

Precomputing Memory Locations for Parametric Allocations

Current worst-case execution time (WCET) analyses do not support programs using dynamic memory allocation. This is mainly due to the unpredictability of cache performance introduced by standard memory allocators. To overcome this problem, algorithms have been proposed that precompute static allocations for dynamically allocating programs with known numeric bounds on the number and sizes of allocated memory blocks. In this paper, we present a novel algorithm for computing such static allocations that can cope with parametric bounds on the number and sizes of allocated blocks. To demonstrate the usefulness of our approach, we precompute static allocations or a set of existing real-time applications and academic examples

Cache-conscious Splitting of MapReduce Tasks and its Application to Stencil Computations

Modern cluster systems are typically composed by nodes with multiple processing units and memory hierarchies comprising multiple cache levels of various sizes. To leverage the full potential of these architectures it is necessary to explore concepts such as parallel programming and the layout of data onto the memory hierarchy. However, the inherent complexity of these concepts and the heterogeneity of the target architectures raises several challenges at application development and performance portability levels, respectively. In what concerns parallel programming, several model and frameworks are available, of which MapReduce [16] is one of the most popular. It was developed at Google [16] for the parallel and distributed processing of large amounts of data in large clusters of commodity machines. Although being very powerful tools, the reference MapReduce frameworks, such as Hadoop and Spark, do not leverage the characteristics of the underlying memory hierarchy. This shortcoming is particularly noticeable in computations that benefit from temporal locality, such as stencil computations. In this context, the goal of this thesis is to improve the performance of MapReduce computations that benefit from temporal locality. To that end we optimize the mapping of MapReduce computations in a machine’s cache memory hierarchy by applying cacheaware tiling techniques. We prototyped our solution on top of the framework Hadoop MapReduce, incorporating a cache-awareness in the splitting stage. To validate our solution and assess its benefits, we developed an API for expressing stencil computations on top the developed framework. The experimental results show that, for a typical stencil computation, our solution delivers an average speed-up of 1.77 while reaching a peek speed-up of 3.2. These findings allows us to conclude that cacheaware decomposition of MapReduce computations considerably boosts the execution of this class of MapReduce computations

Constructive and destructive use of compilers in elliptic curve cryptography

Although cryptographic software implementation is often performed by expert programmers, the range of performance and security driven options, as well as more mundane software engineering issues, still make it a challenge. The use of domain specific language and compiler techniques to assist in description and optimisation of cryptographic software is an interesting research challenge. In this paper we investigate two aspects of such techniques, focusing on Elliptic Curve Cryptography (ECC) in particular. Our constructive results show that a suitable language allows description of ECC based software in a manner close to the original mathematics; the corresponding compiler allows automatic production of an executable whose performance is competitive with that of a hand-optimised implementation. In contrast, we study the worrying potential for naïve compiler driven optimisation to render cryptographic software insecure. Both aspects of our work are set within the context of CACE, an ongoing EU funded project on this general topic

Compiler assisted elliptic curve cryptography

Although cryptographic software implementation is often performed by expert programmers, the range of performance and secu- rity driven options, as well as more mundane software engineering issues, still make it a challenge. The use of domain specific language and com- piler techniques to assist in description and optimisation of cryptographic software is an interesting research challenge. Our results, which focus on Elliptic Curve Cryptography (ECC), show that a suitable language allows description of ECC based software in a manner close to the original mathe- matics; the corresponding compiler allows automatic production of an ex- ecutable whose performance is competitive with that of a hand-optimised implementation. Our work are set within the context of CACE, an ongo- ing EU funded pro ject on this general topic