Solving order constraints in logarithmic space.

We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space

The STAR MAPS-based PiXeL detector

The PiXeL detector (PXL) for the Heavy Flavor Tracker (HFT) of the STAR experiment at RHIC is the first application of the state-of-the-art thin Monolithic Active Pixel Sensors (MAPS) technology in a collider environment. Custom built pixel sensors, their readout electronics and the detector mechanical structure are described in detail. Selected detector design aspects and production steps are presented. The detector operations during the three years of data taking (2014-2016) and the overall performance exceeding the design specifications are discussed in the conclusive sections of this paper

Smart look-ahead arc consistency and the pursuit of CSP tractability

The constraint satisfaction problem (CSP) can be formulated as the problem of deciding, given a pair (A,B) of relational structures, whether or not there is a homomorphism from A to B. Although the CSP is in general intractable, it may be restricted by requiring the “target structure” B to be fixed; denote this restriction by CSP(B). In recent years, much effort has been directed towards classifying the complexity of all problems CSP(B). The acquisition of CSP(B) tractability results has generally proceeded by isolating a class of relational structures B believed to be tractable, and then demonstrating a polynomial-time algorithm for the class. In this paper, we introduce a new approach to obtaining CSP(B) tractability results: instead of starting with a class of structures, we start with an algorithm called look-ahead arc consistency, and give an algebraic characterization of the structures solvable by our algorithm. This characterization is used both to identify new tractable structures and to give new proofs of known tractable structures

Soft constraints: complexity and multimorphisms

Over the past few years there has been considerable progress in methods to systematically analyse the complexity of classical (crisp) constraint satisfaction problems with specified constraint types. One very powerful theoretical development in this area links the complexity of a set of classical constraints to a corresponding set of algebraic operations, known as polymorphisms. In this paper we begin a systematic investigation of the complexity of combinatorial optimisation problems expressed using various forms of soft constraints. We extend the notion of a polymorphism by introducing a more general algebraic operation, which we call a multimorphism. We show that a number of maximal tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms

The expressive rate of constraints

In reasoning tasks involving logical formulas, high expressiveness is desirable, although it often leads to high computational complexity. We study a simple measure of expressiveness: the number of formulas expressible by a language, up to semantic equivalence. In the context of constraints, we prove a dichotomy theorem on constraint languages regarding this measure

Recent results on the algebraic approach to the CSP

Abstract. We describe an algebraic approach to the constraint satisfaction problem (CSP) and present recent results on the CSP that make use of, in an essential way, this algebraic framework.

An Algebraic Approach To Multi-Sorted Constraints

We describe a common framework for the Constraint Satisfaction Problem and the Conjunctive Query Evaluation Problem, encompassing a generalised form of these problems in which different variables may take values from different sets. The framework we develop allows us to specify natural subclasses of these two problems using algebraic techniques, and to establish when these subclasses are tractable. We show that a range of tractable classes can be obtained by combining recently identified tractable subclasses of the usual constraint satisfaction problem over a single set of values. We also systematically develop an algebraic structural theory for the general problem, which provides the prerequisites for further use of the powerful algebraic machinery