Enforcing Arc Consistency on Global Constraints by Solving Subproblems on the Fly

1999 ◽  
pp. 103-117 ◽  
Author(s):  
Christian Bessière ◽  
Jean-Charles Régin
Keyword(s):  
Global Constraints ◽  
Arc Consistency

scholarly journals Soft Constraints of Difference and Equality

2011 ◽  
Vol 41 ◽  
pp. 97-130 ◽  
Author(s):  
E. Hebrard ◽  
D. Marx ◽  
B. O'Sullivan ◽  
I. Razgon
Keyword(s):  
Linear Time ◽  
Combinatorial Problems ◽  
Global Constraints ◽  
Fixed Parameter Tractable ◽  
Common Value ◽  
Arc Consistency ◽  
Standard Cost ◽  
Fixed Parameter ◽  
Difference And Equality ◽  
Np Hardness

In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type, we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however achieving bounds consistency can be done in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor 1/2 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.

Relational Blockworld and Quantum Mechanics

2018 ◽  
Author(s):  
Michael Silberstein ◽  
W.M. Stuckey ◽  
Timothy McDevitt
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Nonlocality ◽  
Global Constraints ◽  
Quantum Superposition ◽  
Delayed Choice ◽  
Counterfactual Definiteness ◽  
Main Thread ◽  
Block Universe ◽  
Contextual Emergence

The main thread of chapter 4 introduces some of the major mysteries and interpretational issues of quantum mechanics (QM). These mysteries and issues include: quantum superposition, quantum nonlocality, Bell’s inequality, entanglement, delayed choice, the measurement problem, and the lack of counterfactual definiteness. All these mysteries and interpretational issues of QM result from dynamical explanation in the mechanical universe and are dispatched using the authors’ adynamical explanation in the block universe, called Relational Blockworld (RBW). A possible link between RBW and quantum information theory is provided. The metaphysical underpinnings of RBW, such as contextual emergence, spatiotemporal ontological contextuality, and adynamical global constraints, are provided in Philosophy of Physics for Chapter 4. That is also where RBW is situated with respect to retrocausal accounts and it is shown that RBW is a realist, psi-epistemic account of QM. All the relevant formalism for this chapter is provided in Foundational Physics for Chapter 4.

Constrained Dual-Level Bandit for Personalized Impression Regulation in Online Ranking Systems

2021 ◽  
Vol 16 (2) ◽  
pp. 1-23
Author(s):  
Zhao Li ◽  
Junshuai Song ◽  
Zehong Hu ◽  
Zhen Wang ◽  
Jun Gao
Keyword(s):  
Optimization Problem ◽  
Initial Conditions ◽  
Global Scale ◽  
Global Constraints ◽  
Economic Losses ◽  
Second Order Cone ◽  
Ranking Systems ◽  
Item Level ◽  
Shopping Experience ◽  
Regulation Method

Impression regulation plays an important role in various online ranking systems, e.g. , e-commerce ranking systems always need to achieve local commercial demands on some pre-labeled target items like fresh item cultivation and fraudulent item counteracting while maximizing its global revenue. However, local impression regulation may cause “butterfly effects” on the global scale, e.g. , in e-commerce, the price preference fluctuation in initial conditions (overpriced or underpriced items) may create a significantly different outcome, thus affecting shopping experience and bringing economic losses to platforms. To prevent “butterfly effects”, some researchers define their regulation objectives with global constraints, by using contextual bandit at the page-level that requires all items on one page sharing the same regulation action, which fails to conduct impression regulation on individual items. To address this problem, in this article, we propose a personalized impression regulation method that can directly makes regulation decisions for each user-item pair. Specifically, we model the regulation problem as a C onstrained D ual-level B andit (CDB) problem, where the local regulation action and reward signals are at the item-level while the global effect constraint on the platform impression can be calculated at the page-level only. To handle the asynchronous signals, we first expand the page-level constraint to the item-level and then derive the policy updating as a second-order cone optimization problem. Our CDB approaches the optimal policy by iteratively solving the optimization problem. Experiments are performed on both offline and online datasets, and the results, theoretically and empirically, demonstrate CDB outperforms state-of-the-art algorithms.

scholarly journals Global constraints on vector-like WIMP effective interactions

2016 ◽  
Vol 2016 (04) ◽  
pp. 015-015 ◽  
Author(s):  
Mattias Blennow ◽  
Pilar Coloma ◽  
Enrique Fernández-Martínez ◽  
Pedro A.N. Machado ◽  
Bryan Zaldívar
Keyword(s):  
Global Constraints ◽  
Effective Interactions

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

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