Abstract
A valued constraint satisfaction problem (VCSP) instance (V;Πω) is a set of variables V with a set of constraints Π weighted by ω. Given a VCSP instance, we are interested in a reweighted subinstance (V;Π'⊃ Π, ω') that preserves the value of the given instance (under every assignment to the variables) within factor 1 ± ∈. A well-studied special case is cut sparsification in graphs, which has found various applications. We show that a VCSP instance consisting of a single boolean predicate P(x, y) (e.g., for cut, P = XOR) can be sparsified into O(|V|=∈2) constraints iff the number of inputs that satisfy P is anything but one (i.e., |P-1(1)| ≠ 1). Furthermore, this sparsity bound is tight unless P is a relatively trivial predicate. We conclude that also systems of 2SAT (or 2LIN) constraints can be sparsified.
| Original language | English |
|---|---|
| Pages (from-to) | 1263-1276 |
| Number of pages | 14 |
| Journal | SIAM Journal on Discrete Mathematics |
| Volume | 31 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2017 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2017 Society for Industrial and Applied Mathematics.
Funding
The first author was partially supported by the Lynn and William Frankel Center for Computer Sciences. The second author's work was supported in part by Israel Science Foundation grant 897/13 and US-Israel BSF grant 2010418.
| Funders | Funder number |
|---|---|
| Lynn and William Frankel Center for Computer Sciences | |
| US-Israel BSF | 2010418 |
| Israel Science Foundation | 897/13 |
Keywords
- Boolean predicates
- Cut sparsification
- MAX-CSP
- Valued constraint satisfaction problem