Many of standard practical techniques of solving constraint satisfaction problems use various decomposition methods to represent a problem as a combination of smaller ones. We study a general method of decomposing constraint satisfaction problems in which every constraint is represented as a disjunction of two or more simpler constraints defined, possibly, on smaller sets of values. We call a p...

In the algebraic approach to CSP (Constraint Satisfaction Problem), the complexity of constraint languages is studied using closure operations called polymorphisms. Many of these operations are known to induce tractability of any language they preserve. We focus on the meta-problem: given a language Γ, decide if Γ has a polymorphism with nice properties. We design an algorithm that decides in p...

In recent years, symmetry breaking for constraint satisfaction problems (CSPs) has attracted considerable attention. Various general schemes have been proposed to eliminate symmetries. In general, these schemes may take exponential space or time to eliminate all the symmetries. We identify several classes of CSPs that encompass many practical problems and for which symmetry breaking for various...

Reformulating constraint satisfaction problems (CSPs) in lower arity is a common procedure when computing consistency. Lower arity CSPs are simpler to treat than high arity CSPs. Several consistency algorithms have exponential complexity in the CSP’s arity, others only work on low

There is an extensive literature on the complexity of planning, but explicit bounds on time and space complexity are very rare. On the other hand, problems like the constraint satisfaction problem (CSP) have been thoroughly analysed in this respect. We provide a number of upperand lower-bound results (the latter based on various complexitytheoretic assumptions such as the Exponential Time Hypot...

In this paper, an approximate solution of sensitivity matrix of required velocity with final velocity constraint is derived using a piecewise linear gravity assumption. The total flight time is also fixed for the problem. Simulation results show the accuracy of the method. Increasing the midway points for linearization, increases the accuracy of the solution, which this, in turn, depends on the...

We further generalise a construction – the fibre construction – that was developed in an earlier paper of the first two authors. The extension in this paper gives a polynomial-time reduction of CSP(H) for any relational system H to CSP(P ) for any relational system P that meets a certain technical partition condition, that of being K3-partitionable. Moreover, we define an equivalent condition o...

We study the time complexity of (d, k)-CSP, the problem of deciding satisfiability of a constraint system C with n variables, domain size d, and at most k variables per constraint. We are interested in the question how the domain size d influences the complexity of deciding satisfiability. We show, assuming the Exponential Time Hypothesis, that two special cases, namely (d, 2)-CSP with bounded ...