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Additive Sparsification of CSPs

Authors Eden Pelleg, Stanislav Živný

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Author Details

Eden Pelleg
  • Mathematical Institute, University of Oxford, UK
Stanislav Živný
  • Department of Computer Science, University of Oxford, UK

Funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 714532). The paper reflects only the authors' views and not the views of the ERC or the European Commission. The European Union is not liable for any use that may be made of the information contained therein.
  • Živný, Stanislav: Royal Society University Research Fellowship.

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Eden Pelleg and Stanislav Živný. Additive Sparsification of CSPs. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.75

Abstract

Multiplicative cut sparsifiers, introduced by Benczúr and Karger [STOC'96], have proved extremely influential and found various applications. Precise characterisations were established for sparsifiability of graphs with other 2-variable predicates on Boolean domains by Filtser and Krauthgamer [SIDMA'17] and non-Boolean domains by Butti and Živný [SIDMA'20].
Bansal, Svensson and Trevisan [FOCS'19] introduced a weaker notion of sparsification termed "additive sparsification", which does not require weights on the edges of the graph. In particular, Bansal et al. designed algorithms for additive sparsifiers for cuts in graphs and hypergraphs.
As our main result, we establish that all Boolean Constraint Satisfaction Problems (CSPs) admit an additive sparsifier; that is, for every Boolean predicate P:{0,1}^k → {0,1} of a fixed arity k, we show that CSP(P)} admits an additive sparsifier. Under our newly introduced notion of all-but-one sparsification for non-Boolean predicates, we show that CSP(P)} admits an additive sparsifier for any predicate P:D^k → {0,1} of a fixed arity k on an arbitrary finite domain D.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Sparsification and spanners
Keywords
  • additive sparsification
  • graphs
  • hypergraphs
  • minimum cuts

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