Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

Abstract

This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns.

An Evaluation of Heuristic Methods for the Bandwidth Reduction of Large-Scale Graphs

“…In tables in this subsection, β 0 denotes the original bandwidth of the matrix. Oliveira & Silva, 2019, 2021 As previously mentioned, the ACHH system (Gonzaga de Oliveira & Silva, 2019, 2021 is the current state-of-the-art strategy regarding low-cost heuristics for bandwidth reduction when considering the running times as a pertinent characteristic of the appraisal. Table 1 summarizes the results presented by a previous effort (Gonzaga de Oliveira & Carvalho, 2022) comparing the GPS, FNCHC+, ILS-band, and ACHH heuristics when applied to 10 matrices with sizes ranging from 70,656 to 1,585,478.…”

“…Gonzaga de Oliveira & Silva (2021) incorporated a local search into the approach and yielded even better results when executed with symmetric instances. Thus, when considering the running times as a relevant feature of the evaluation, the ACHH system (Gonzaga de Oliveira & Silva, 2019, 2021 is the current state-of-the-art strategy regarding low-cost heuristics for bandwidth reduction.…”

“…One of these efforts is to reduce the graph bandwidth. Thus, one can relate the bandwidth reduction problem to Unifesp, São Paulo, SP, Brazil -E-mail: sanderson.oliveira@unifesp.br -https://orcid.org/0000-0003-4863-542X a broad scope of significant practical applications in various application domains in engineering, science, industry, and technology (Gonzaga de Oliveira & Silva, 2021).…”

An OpenMP‐based breadth‐first search implementation using the bag data structure

“…In particular, the Graph500 benchmark suite 4 and several other high‐performance computing platform benchmarking 2 include BFS as a kernel component. As another example, state‐of‐the‐art low‐cost heuristics for large‐scale matrix bandwidth reduction are variants or apply the BFS algorithm 5–9 …”

“…As another example, state-of-the-art low-cost heuristics for large-scale matrix bandwidth reduction are variants or apply the BFS algorithm. [5][6][7][8][9] The serial BFS version, implemented with the queue data structure, is fast and efficient, demanding time (|V| + |E|) for the graph G. The constants hidden by the asymptotic notation are small because of the simplicity of queue operations: inserting at the end of the queue and removing from the beginning of the data structure are Θ(1) operations.…”