Nowadays, many real problems in artificial intelligence can be modelled as constraint satisfaction problems (CSPs). A general CSP is known to be NP-complete. Nevertheless, distributed models may reduce the exponential complexity by partitioning the problem into a set of subproblems. In this paper, we present a preprocess technique to break a single large problem into a set of smaller loosely co...

Some n-ary constraints such as the alldiff constraints arise naturally in real fife constraint satisfaction problems (CSP). General purpose filtering algorithms could be applied to such constraints. By taking the semantics of the constraint into account, it is possible to design more efficient filtering algorithms. When the domains of the variables are totally ordered (e.g. all values are integ...

We introduce groupoids – generalisations of groups in which not all pairs of elements may be multiplied, or, equivalently, categories in which all morphisms are invertible – as the appropriate algebraic structures for dealing with conditional symmetries in Constraint Satisfaction Problems (CSPs). We formally define the Full Conditional Symmetry Groupoid associated with any CSP, giving bounds fo...

We study the complexity of valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a constraint language, a fixed set of cost functions over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimise the sum. We consider the case of so-called conservative languages; that is, languages containi...

We determine the complexity of several constraint-satisfaction problems using the heuristic algorithm WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models studied, the hardest for WalkSAT is the one for which there is a polynomial time algorithm.

We give the first logarithmic approximation for minimizing average flow-time of jobs in the subset parallel machine setting (also called the restricted assignment setting) under a single knapsack constraint. In a knapsack constraint setting, each job has a profit, and the set of jobs which get scheduled must have a total profit of at least a quantity Π. Our result extends the work of Gupta, Kri...

In previous works we have shown that linear logic with subexponentials (SELL), a refinement of linear logic, can be used to specify emergent features of concurrent constraint programming (CCP) languages, such as preferences and spatial, epistemic and temporal modalities. In order to do so, we introduced a number of extensions to SELL, such as subexponential quantifiers for the specification of ...

Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved [4, 18] that if a constraint language has a weak near unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, otherwise it is NPcomplete. In the paper we present a modification of the a...

A key task in combinatorial optimisation is the minimisation of discrete functions. Important examples are submodular functions, see e. g. [6, 13, 14, 17], and bisubmodular functions, see e. g. [2, 6, 14, 16]. These functions can be viewed as (special) functions from D to R where D is a 2-element set for the submodular case and a 3-element set for the bisubmodular case. Fix a finite set D. One ...

Many problems of theoretical and practical interest can be formulated as Constraint Satisfaction Problems (CSPs). The general CSP is known to be NP-complete; however, distributed models may reduce the exponential complexity by partitioning the problem into a set of subproblems. In this work, we present a distributed model for solving large-scale CSPs in which agents are committed to sets of con...