9,433 research outputs found
The power of Sherali-Adams relaxations for general-valued CSPs
We give a precise algebraic characterisation of the power of Sherali-Adams
relaxations for solvability of valued constraint satisfaction problems to
optimality. The condition is that of bounded width which has already been shown
to capture the power of local consistency methods for decision CSPs and the
power of semidefinite programming for robust approximation of CSPs.
Our characterisation has several algorithmic and complexity consequences. On
the algorithmic side, we show that several novel and many known valued
constraint languages are tractable via the third level of the Sherali-Adams
relaxation. For the known languages, this is a significantly simpler algorithm
than the previously obtained ones. On the complexity side, we obtain a
dichotomy theorem for valued constraint languages that can express an injective
unary function. This implies a simple proof of the dichotomy theorem for
conservative valued constraint languages established by Kolmogorov and Zivny
[JACM'13], and also a dichotomy theorem for the exact solvability of
Minimum-Solution problems. These are generalisations of Minimum-Ones problems
to arbitrary finite domains. Our result improves on several previous
classifications by Khanna et al. [SICOMP'00], Jonsson et al. [SICOMP'08], and
Uppman [ICALP'13].Comment: Full version of an ICALP'15 paper (arXiv:1502.05301
Propagators and Violation Functions for Geometric and Workload Constraints Arising in Airspace Sectorisation
Airspace sectorisation provides a partition of a given airspace into sectors,
subject to geometric constraints and workload constraints, so that some cost
metric is minimised. We make a study of the constraints that arise in airspace
sectorisation. For each constraint, we give an analysis of what algorithms and
properties are required under systematic search and stochastic local search
Revisiting the Linear Programming Relaxation Approach to Gibbs Energy Minimization and Weighted Constraint Satisfaction
We present a number of contributions to the LP relaxation approach to weighted constraint satisfaction (= Gibbs energy minimization). We link this approach to many works from constraint programming, which relation has so far been ignored in machine vision and learning. While the approach has been mostly considered only for binary constraints, we generalize it to n-ary constraints in a simple and natural way. This includes a simple algorithm to minimize the LP-based upper bound, n-ary max-sum diffusion – however, we consider using other bound-optimizing algorithms as well. The diffusion iteration is tractable for a certain class of higharity constraints represented as a black-box, which is analogical to propagators for global constraints CSP. Diffusion exactly solves permuted n-ary supermodular problems. A hierarchy of gradually tighter LP relaxations is obtained simply by adding various zero constraints and coupling them in various ways to existing constraints. Zero constraints can be added incrementally, which leads to a cutting plane algorithm. The separation problem is formulated as finding an unsatisfiable subproblem of a CSP
Empirical evaluation of Soft Arc Consistency algorithms for solving Constraint Optimization Problems
A large number of problems in Artificial Intelligence and other areas of science can be viewed as special cases of constraint satisfaction or optimization problems. Various approaches have been widely studied, including search, propagation, and heuristics. There are still challenging real-world COPs that cannot be solved using current methods. We implemented and compared several consistency propagation algorithms, which include W-AC*2001, EDAC, VAC, and xAC. Consistency propagation is a classical method to reduce the search space in CSPs, and has been adapted to COPs. We compared several consistency propagation algorithms, based on the resemblance between the optimal value ordering and the approximate value ordering generated by them. The results showed that xAC generated value orderings of higher quality than W-AC*2001 and EDAC. We evaluated some novel hybrid methods for solving COPs. Hybrid methods combine consistency propagation and search in order to reach a good solution as soon as possible and prune the search space as much as possible. We showed that the hybrid method which combines the variant TP+OnOff and branch-and-bound search performed fewer constraint checks and searched fewer nodes than others in solving random and real-world COPs
Uncertainty in Soft Temporal Constraint Problems:A General Framework and Controllability Algorithms forThe Fuzzy Case
In real-life temporal scenarios, uncertainty and preferences are often
essential and coexisting aspects. We present a formalism where quantitative
temporal constraints with both preferences and uncertainty can be defined. We
show how three classical notions of controllability (that is, strong, weak, and
dynamic), which have been developed for uncertain temporal problems, can be
generalized to handle preferences as well. After defining this general
framework, we focus on problems where preferences follow the fuzzy approach,
and with properties that assure tractability. For such problems, we propose
algorithms to check the presence of the controllability properties. In
particular, we show that in such a setting dealing simultaneously with
preferences and uncertainty does not increase the complexity of controllability
testing. We also develop a dynamic execution algorithm, of polynomial
complexity, that produces temporal plans under uncertainty that are optimal
with respect to fuzzy preferences
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