Calendar management tools assist users with coordinating their daily life. Different tasks have to be scheduled according to the user preferences. In many cases, tasks are at different locations and travel times have to be considered. Therefore, these kinds of calendar management problems can be regarded as spatio-temporal optimisation problems and are often variants of traveling salesman problems (TSP) or vehicle routing problems. While standard TSPs require a solution to include all tasks, prize-collecting TSPs are more suited for calendar management problems as they require a solution that optimises the total sum of prizes we assigned to tasks at different locations. If we now add time windows that limit when tasks can occur, these prize-collecting TSPs with time windows (TW-TSP) are excellent abstractions of spatio-temporal optimisation problems such as calendar management. Due to the inherent complexity of TW-TSPs, the existing literature considers mainly approximation algorithms or special cases. We present a novel algorithm for TW-TSPs that enables us to find the optimal solution to TW-TSP problems occurring in real-world calendar management applications efficiently. Our algorithm is a fixed-parameter tractable algorithm that depends on the maximal number of tasks that can be revisited from some other task, a parameter which is small in the application scenario we consider.

CP-networks have been proposed as a simple and intuitive graphical tool for representing conditional ceteris paribus preference statements over the values of a set of variables. While the problem of reasoning with CP-networks has been receiving some attention, there are very few works that address the problem of learning CP-networks. In this work we investigate the task of learning CP-networks, given access to a set of pairwise comparisons. We first prove that the learning problem is intractable, even under several simplifying assumptions. We then present an algorithm that, under certain assumptions about the observed pairwise comparisons, identifies a CP-network that entails these comparisons. We finally show that the proposed algorithm is a PAC-learner, and, thus, that the CP-networks it induces accurately predict the user's preferences on previously unseen situations.

While there are several languages for representing combinatorial preferences over sets of alternatives, none of these are well-suited to the representation of ordinal preferences over sets of goods (which are typically required to be monotonic). We propose such a language, taking inspiration from previous work on graphical languages for preference representation, specifically CP-nets, and introduce conditional importance networks (CI-nets).  A CI-net includes statements of the form "if I have a set A of goods, and I do not have any of the goods from some other set B, then I prefer the set of goods C over the set of goods D." We investigate expressivity and complexity issues for CI-nets. Then we show that CI-nets are well-suited to the description of fair division problems.

Voting theory can provide useful insights for multiagent preference aggregation. However, the standard setting assumes voters with preferences that are total orders, as well as a ballot language that coincides with the preference language. In typical AI scenarios, these assumptions do not hold: certain alternatives may be incomparable for some agents, and others may have their preferences encoded in a format that is different from how the preference aggregation mechanism wants them. We study the consequences of dropping these assumptions. In particular, we investigate the consequences for the important notion of strategy-proofness. While strategy-proofness cannot be guaranteed in the classical setting, we are able to show that there are situations in our more general framework where this is possible. We also consider computational aspects of the problem.

This paper deals with Decision-Making in the context of multiattribute utility theory and, more precisely, with the problem of efficiently determining the best alternative w.r.t. an agent's preferences (choice problem). We assume that alternatives are elements of a product set of attributes and that the agent's preferences are represented by a generalized additive decomposable (GAI) utility on this set. Such a function allows an efficient representation of interactions between attributes while preserving some decomposability of the model. GAI utilities can be compiled into graphical structures called GAI networks that can be exploited to solve choice problems using collect/distribute schemes essentially similar to those used in Bayesian networks. In this paper, rather than directly using this scheme on the GAI network for determining the most preferred alternative, we propose to work with another GAI function, acting as an upper-bound on utility values and enhancing the model's decomposability. This method still provides the exact optimal solution but speeds up significantly the search. It proves to be particularly useful when dealing with choice and ranking under constraints and within collective Decision-Making, where GAI nets tend to have a large size. We present an efficient algorithm for determining this new GAI function and provide experimental results highlighting the practical efficiency of our procedure.

Hard and soft precedence constraints  play  a key role in many application domains.  In telecommunications, one application is the configuration of call control feature subscriptions  where the task is to sequence a set of user-selected features subject to a set of hard (catalogue) precedence constraints and a set of soft (user-selected) precedence constraints. When no such consistent sequence exists, the task is to find an optimal relaxation by discarding some  features or user precedences. For this purpose, we present the global constraint SOFTPREC. Enforcing Generalized Arc Consistency  (GAC)  on SOFTPREC is NP-complete. Therefore, we approximate  GAC based on domain pruning  rules that follow from the semantics of  SOFTPREC; this pruning is polynomial. Empirical results demonstrate  that  the search effort  required by SOFTPREC is  up to one order of magnitude less than  the previously known best CP approach for the feature subscription problem. SOFTPREC is also applicable to other  problem domains  including minimum  cutset problems  for which initial experiments confirm the interest.

We study under what conditions bound consistency (BC) and arc consistency  (AC),  two forms of propagation used in constraint solvers, are equivalent to each other. We show that they prune exactly the same values when the propagated constraint is connected row convex / closed under median and its complement is row convex. This  characterization is exact for binary constraints. Since row convexity depends on the order of the values in the domains, we give polynomial algorithms for computing orders under which BC and AC are equivalent, if any.

Qualitative Spatial and Temporal Reasoning (QSR) is concerned with constraint-based formalisms for representing, and reasoning with, spatial and temporal information over infinite domains.  Within the QSR community it has been a widely accepted assumption that genuine qualitative reasoning methods outperform other reasoning methods that are applicable to encodings of qualitative CSP instances. Recently this assumption has been tackled by several authors, who proposed to encode qualitative CSP instances as finite CSP or SAT instances. In this paper we report on the results of a broad empirical study in which we compared the performance of several reasoners on instances from different qualitative formalisms. Our results show that for small-sized qualitative calculi (e.g., Allen's interval algebra and RCC-8) a state-of-the-art implementation of QSR methods currently gives the most efficient performance. However, on recently suggested large-size calculi, e.g., OPRA4, finite CSP encodings provide a considerable performance gain. These results confirm a conjecture by Bessière stating that support-based constraint propagation algorithms provide better performance for large-sized qualitative calculi.

Set variables in constraint satisfaction problems (CSPs) are typically propagated by enforcing set bounds consistency together with cardinality reasoning, which uses some inference rules involving the cardinality of a set variable to produce more prunings than set bounds propagation alone. Multiset variables are a generalization of set variables by allowing the elements to have repetitions. In this paper, we generalize cardinality reasoning for multiset variables. In addition, we propose to exploit the variety of a multiset — the number of distinct elements in it — to improve modeling expressiveness and further enhance constraint propagation. We derive a number of inference rules involving the varieties of multiset variables. The rules interact varieties with the traditional components of multiset variables (such as cardinalities) to obtain stronger propagation. We also demonstrate how to apply the rules to perform variety reasoning on some common multiset constraints. Experimental results show that performing variety reasoning on top of cardinality reasoning can effectively reduce more search space and achieve better runtime in solving multiset CSPs.

We introduce planning games, a study of interactions of self-motivated agents in automated planning settings. Planning games extend STRIPS-like models of single-agent planning to systems of multiple self-interested agents, providing a rich class of structured games that capture subtle forms of local interactions. We consider two basic models of planning games and adapt game-theoretic solution concepts to these models.  In both models, agents may need to cooperate in order to achieve their goals, but are assumed to do so only in order to increase their net benefit. For each model we study the computational problem of finding a stable solution and provide efficient algorithms for systems exhibiting acyclic interaction structure.