DeepAI AI Chat
Log In Sign Up

Additive Sparsification of CSPs

by   Eden Pelleg, et al.

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.


page 1

page 2

page 3

page 4


Beyond Boolean Surjective VCSPs

Fulla, Uppman, and Zivny [ACM ToCT'18] established a dichotomy theorem f...

Sparsification of Binary CSPs

A cut ε-sparsifier of a weighted graph G is a re-weighted subgraph of G ...

Fast Construction of 4-Additive Spanners

A k-additive spanner of a graph is a subgraph that preserves the distanc...

Domain Semirings United

Domain operations on semirings have been axiomatised in two different wa...

On uncertainty inequalities related to subcube partitions and additive energy

The additive energy plays a central role in combinatorial number theory....

Influence of a Set of Variables on a Boolean Function

The influence of a set of variables on a Boolean function has three sepa...

Boolean symmetric vs. functional PCSP dichotomy

Given a 3-uniform hypergraph (V,E) that is promised to admit a {0,1}-col...