Sparse data structures are ubiquitous in modern computing, and numerous formats have been designed to represent them. These formats may exploit specific sparsity patterns, aiming to achieve higher performance for key numerical computations than more general-purpose formats such as CSR and COO. In this work presents UZP, a new sparse format based on polyhedral sets of integer points. UZP is a flexible format that subsumes CSR, COO, DIA, BCSR, etc., by raising them to a common mathematical abstraction: a union of integer polyhedra, each intersected with an affine lattice. We present a modular approach to building and optimizing UZP: it captures equivalence classes for the sparse structure, enabling the tuning of the representation for target-specific and application-specific performance considerations. UZP is built from any input sparse structure using integer coordinates, and is interoperable with existing software using CSR and COO data layouts. We provide detailed performance evaluation of UZP on 200+ matrices from SuiteSparse, demonstrating how simple and mostly unoptimized generic executors for UZP can already achieve solid performance by exploiting 𝒵-polyhedra structures.

The main objective of this work is to bring supercomputing and parallel processing closer to non-specialized audiences by building a Raspberry Pi cluster, called Clupiter, which emulates the operation of a supercomputer. It consists of eight Raspberry Pi devices interconnected to each other so that they can run jobs in parallel. To make it easier to show how it works, a web application has been developed. It allows launching parallel applications and accessing a monitoring system to see the resource usage when these applications are running. The NAS Parallel Benchmarks (NPB) are used as demonstration applications. From this web application a couple of educational videos can also be accessed. They deal, in a very informative way, with the concepts of supercomputing and parallel programming.