Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

Conference · Fri Dec 17 04:00:00 EST 2021

DOI:https://doi.org/10.1109/HiPC53243.2021.00045· OSTI ID:1861987

Liu, Xu ^[1]; Firoz, Jesun S. ^[2]; Lumsdaine, Andrew ^[2]; Joslyn, Cliff A. ^[2]; Aksoy, Sinan G. ^[2]; Praggastis, Brenda L. ^[2]; Gebremedhin, Assefaw ^[3]

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1. WASHINGTON STATE UNIV
2. BATTELLE (PACIFIC NW LAB)
3. Washington State University

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$$s$$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $$s$$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $$s$$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $$s$$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $$s$$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $$10\times$$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $$s$$ value).

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1861987
• Report Number(s): PNNL-SA-164086
• Country of Publication: United States
• Language: English

Related Subjects

hypergraph algorithms
graph algorithms
parallel algorithms