eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-01-08
49:1
49:21
10.4230/LIPIcs.ITCS.2019.49
article
SOS Lower Bounds with Hard Constraints: Think Global, Act Local
Kothari, Pravesh K.
1
O'Donnell, Ryan
2
Schramm, Tselil
3
Department of Computer Science, Princeton University and Institute for Advanced Study, Princeton, USA
Department of Computer Science, Carnegie Mellon University, Pittsburgh, USA
Department of Computer Science, Harvard and MIT, Cambridge, USA
Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a "cardinality constraint", as in, say, the Min-Bisection problem. Second, while the pseudoexpectation of the objective function was shown to have some value beta, it did not necessarily actually "satisfy" the constraint "objective = beta". In this paper we show how to remedy both deficiencies in the case of random CSPs, by translating global constraints into local constraints. Using these ideas, we also show that degree-Omega(sqrt{n}) SOS does not provide a (4/3 - epsilon)-approximation for Min-Bisection, and degree-Omega(n) SOS does not provide a (11/12 + epsilon)-approximation for Max-Bisection or a (5/4 - epsilon)-approximation for Min-Bisection. No prior SOS lower bounds for these problems were known.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol124-itcs2019/LIPIcs.ITCS.2019.49/LIPIcs.ITCS.2019.49.pdf
sum-of-squares hierarchy
random constraint satisfaction problems