174 research outputs found
On The Relational Width of First-Order Expansions of Finitely Bounded Homogeneous Binary Cores with Bounded Strict Width
The relational width of a finite structure, if bounded, is always (1,1) or
(2,3). In this paper we study the relational width of first-order expansions of
finitely bounded homogeneous binary cores where binary cores are structures
with equality and some anti-reflexive binary relations such that for any two
different elements a, b in the domain there is exactly one binary relation R
with (a, b) in R.
Our main result is that first-order expansions of liberal finitely bounded
homogeneous binary cores with bounded strict width have relational width (2,
MaxBound) where MaxBound is the size of the largest forbidden substructure, but
is not less than 3, and liberal stands for structures that do not forbid
certain finite structures of small size. This result is built on a new approach
and concerns a broad class of structures including reducts of homogeneous
digraphs for which the CSP complexity classification has not yet been obtained.Comment: A long version of an extended abstract that appeared in LICS 202
Approximating optimal transport with linear programs
In the regime of bounded transportation costs, additive approximations for
the optimal transport problem are reduced (rather simply) to relative
approximations for positive linear programs, resulting in faster additive
approximation algorithms for optimal transport.Comment: To appear in SOSA 201
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