Manipulation and bribery have received much attention from the social choice community. We consider these concepts in the setting of preference formalisms, where the Pareto principle is used to assign to preference theories collections of optimal outcomes, rather than a single winning outcome as is common in social choice. We adapt the concepts of manipulation and bribery to this setting. We provide characterizations of situations when manipulation and bribery are possible. Assuming a particular logical formalism for expressing preferences, we establish the complexity of determining a possibility for manipulation or bribery. In all cases that do not in principle preclude a possibility of manipulation or bribery, our complexity results show that deciding whether manipulation or bribery are actually possible is computationally hard.

Real-world decisions involve preferences that are nonlinear and often defined over multiple and interdependent issues. Such scenarios are known to be challenging, especially in strategic encounters between agents having distinct constraints and preferences. In this case, reaching an agreement becomes more difficult as the search space and the complexity of the problem grow. In this paper, we propose a new representation for constraint-based utility spaces that can tackle the scalability problem by efficiently finding the optimal contracts. Particularly, the constraint-based utility space is mapped into an issue-constraint hyper-graph. Exploring the utility space reduces then to a message passing mechanism along the hyper-edges by means of utility propagation. We experimentally evaluate the model using parameterized random nonlinear utility spaces. We show that it can handle a large family of complex utility spaces by finding the optimal contract(s), outperforming previous sampling-based approaches.

We introduce a novel qualitative preference representation language, preference trees , or P-trees . We show that the lan- guage is intuitive to specify preferences over combinatorial domains and it extends existing preference formalisms such as LP-trees , ASO-rules and possibilistic logic . We study rea- soning problems with P-trees and obtain computational com- plexity results.

Markov processes are widely used to generate sequences that imitate a given style, using random walk. Random walk generates sequences by iteratively concatenating states to prefixes of length equal or less than the given Markov order}. However, at higher orders, Markov chains tend to replicate chunks of the corpus with a size possibly higher than the order, a primary form of plagiarism. The Markov order defines a maximum length for training but not for generation. In the framework of constraint satisfaction (CSP), we introduce MaxOrder. This global constraint ensures that generated sequences do not include chunks larger than a given maximum order. We exhibit an automaton that recognises the solution set, with a size linear in the size of the corpus. We propose a linear-time procedure to generate this automaton from a corpus and a given max order. We then use this automaton to achieve generalised arc consistency for the MaxOrder constraint, holding on a sequence of size n, in O(n.T) time, where T is the size of the automaton. We illustrate our approach by generating text sequences from text corpora with a maximum order guarantee, effectively controlling plagiarism.

Decomposition is a technique to obtain complete solutions by assembling independently obtained partial solutions. In particular, constraint decomposition plays an important role in distributed databases, distributed scheduling and violation detection: It enables conflict-free local decision making, while avoiding communication overloading. One of the main issues in decomposition is the loss of flexibility due to decomposition. Here, flexibility roughly refers to the freedom in choosing suitable values for the variables in order to satisfy the constraints. In this paper, we concentrate on linear constraint systems and efficient decomposition techniques for them. Using a generalization of a flexibility metric developed for Simple Temporal Networks, we show how an efficient decomposition technique for linear constraint systems can be derived that minimizes the loss of flexibility. As a by-product of this decomposition technique, we propose an intuitively attractive flexibility metric for linear constraint systems where decomposition does not incur any loss of flexibility.

The problem of checking the consistency of spatial calculi that contain both unknown and known entities (constants, i.e., real geometries) has recently been studied. Until now, all the approaches are theoretical and no implementation has been proposed. In this paper we present the first reasoner that takes as input RCC-5 or RCC-8 networks with variables and constants and decides their consistency. We investigate the performance of the reasoner experimentally using real-world networks and show that we can achieve significantly better times by geometry simplification and parallelization.

There has been a great deal of interest about negotiations having interdependent issues and nonlinear utility spaces as they arise in many realistic situations. In this case, reaching a consensus among agents becomes more difficult as the search space and the complexity of the problem grow. Nevertheless, none of the proposed approaches tries to quantitatively assess the complexity of the scenarios in hand, or to exploit the topology of the utility space necessary to concretely tackle the complexity and the scaling issues. We address these points by adopting a representation that allows a modular decomposition of the issues and constraints by mapping the utility space into an issue-constraint hypergraph. Exploring the utility space reduces then to a message passing mechanism along the hyperedges by means of utility propagation. Adopting such representation paradigm will allow us to rigorously show how complexity arises in nonlinear scenarios. To this end, we use the concept of information entropy in order to measure the complexity of the hypergraph. Being able to assess complexity allows us to improve the message passing algorithm by adopting a low-complexity propagation scheme. We evaluated our model using parametrized random hyper- graphs, showing that it can optimally handle complex utility spaces while outperforming previous sampling approaches.

In this paper, we describe a simple randomized algorithm that runs in polynomial time and solves connected row convex (CRC) constraints in distributed settings. CRC constraints generalize many known tractable classes of constraints like 2-SAT and implicational constraints. They can model problems in many domains including temporal reasoning and geometric reasoning, and generally speaking, play the role of ``Gaussians'' in the logical world. Our simple randomized algorithm for solving them in distributed settings, therefore, has a number of important applications. We support our claims through a theoretical analysis and empirical results.

Backdoor sets represent clever reasoning shortcuts through the search space for SAT and CSP. By instantiating the backdoor variables one reduces the given instance to several easy instances that belong to a tractable class.The overall time needed to solve the instance is exponential in the size of the backdoor set, hence it is a challenging problem to find a small backdoor set if one exists; over the last years this problem has been subject of intensive research. In this paper we extend the classical notion of a strong backdoor set by allowing that different instantiations of the backdoor variables result in instances that belong to different base classes; the union of the base classes forms a heterogeneous base class. Backdoor sets to heterogeneous base classes can be much smaller than backdoor sets to homogeneous ones, hence they are much more desirable but possibly harder to find. We draw a detailed complexity landscape for the problem of detecting strong backdoor sets into heterogeneous base classes for SAT and CSP. We provide algorithms that establish fixed-parameter tractability under natural parameterizations, and we contrast the tractability results with hardness results that pinpoint the theoretical limits. Our results apply to the current state-of-the-art of tractable classes of CSP and SAT that are definable by restricting the constraint language.

Bi-Objective Combinatorial Optimization problems are ubiquitous in real-world applications and designing approaches to solve them efficiently is an important research area of Artificial Intelligence. In Constraint Programming, the recently introduced bi-objective Pareto constraint allows one to solve bi-objective combinatorial optimization problems exactly. Using this constraint, every non-dominated solution is collected in a single tree-search while pruning sub-trees that cannot lead to a non-dominated solution. This paper introduces a simpler and more efficient filtering algorithm for the bi-objective Pareto constraint. The efficiency of this algorithm is experimentally confirmed on classical bi-objective benchmarks.