Piecewise Linear Valued CSPs Solvable by Linear Programming Relaxation

The Power of Linear Programming for General-Valued CSPs

Let D, called the domain, be a fixed finite set and let Γ, called the valued constraint language, be a fixed set of functions of the form f : D → Q ∪ {∞}, where different functions might have different arity m. We study the valued constraint satisfaction problem parametrised by Γ, denoted by VCSP(Γ). These are minimisation problems given by n variables and the objective function given by a sum ...

Linear Programming and the Complexity of Finite-valued CSPs

We consider the complexity classification project for the valued constraint satisfaction problem (VCSP) restricted to rational-valued cost functions. A year ago, classifications were known for Boolean domains and for the case when all unary cost functions are allowed. In the time that has passed since then, there has been significant progress in the area. In this paper, we describe the full com...

The power of linear programming for valued CSPs: a constructive characterization

A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BL...

Piecewise Linear Dynamic Programming for Constrained POMDPs

We describe an exact dynamic programming update for constrained partially observable Markov decision processes (CPOMDPs). State-of-the-art exact solution of unconstrained POMDPs relies on implicit enumeration of the vectors in the piecewise linear value function, and pruning operations to obtain a minimal representation of the updated value function. In dynamic programming for CPOMDPs, each vec...

Piecewise Constant Controlled Linear Fuzzy Systems