What question did this study set out to answer?

The aim is to develop a dynamic algorithm for maintaining spectral sparsifiers of directed hypergraphs.

February 27, 2026Open Access

Fully Dynamic Spectral Sparsification for Directed Hypergraphs

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This algorithm maintains efficient spectral hypergraph sparsifiers in directed hypergraphs, suggesting a novel approach to sparsification.

The aim is to develop a dynamic algorithm for maintaining spectral sparsifiers of directed hypergraphs.
Introduced a fully dynamic algorithm for spectral hypergraph sparsification.
Achieved near-optimal sparsifier size with specific bounds on vertices and hyperedges.
Extended approach to handle batch-dynamic settings for hyperedge modifications.
Achieved an amortized update time of O(r² log ³ m).
Maintained sparsifiers with size O(n² / ε ² log ⁷ m).
Processed batches of hyperedge insertions or deletions with O(kr² log ³ m) work.

Forster et al. (2026) studied this question.

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This algorithm maintains efficient spectral hypergraph sparsifiers in directed hypergraphs, suggesting a novel approach to sparsification.