280 research outputs found
Tree Projections and Structural Decomposition Methods: Minimality and Game-Theoretic Characterization
Tree projections provide a mathematical framework that encompasses all the
various (purely) structural decomposition methods that have been proposed in
the literature to single out classes of nearly-acyclic (hyper)graphs, such as
the tree decomposition method, which is the most powerful decomposition method
on graphs, and the (generalized) hypertree decomposition method, which is its
natural counterpart on arbitrary hypergraphs. The paper analyzes this
framework, by focusing in particular on "minimal" tree projections, that is, on
tree projections without useless redundancies. First, it is shown that minimal
tree projections enjoy a number of properties that are usually required for
normal form decompositions in various structural decomposition methods. In
particular, they enjoy the same kind of connection properties as (minimal) tree
decompositions of graphs, with the result being tight in the light of the
negative answer that is provided to the open question about whether they enjoy
a slightly stronger notion of connection property, defined to speed-up the
computation of hypertree decompositions. Second, it is shown that tree
projections admit a natural game-theoretic characterization in terms of the
Captain and Robber game. In this game, as for the Robber and Cops game
characterizing tree decompositions, the existence of winning strategies implies
the existence of monotone ones. As a special case, the Captain and Robber game
can be used to characterize the generalized hypertree decomposition method,
where such a game-theoretic characterization was missing and asked for. Besides
their theoretical interest, these results have immediate algorithmic
applications both for the general setting and for structural decomposition
methods that can be recast in terms of tree projections
Tractable Optimization Problems through Hypergraph-Based Structural Restrictions
Several variants of the Constraint Satisfaction Problem have been proposed
and investigated in the literature for modelling those scenarios where
solutions are associated with some given costs. Within these frameworks
computing an optimal solution is an NP-hard problem in general; yet, when
restricted over classes of instances whose constraint interactions can be
modelled via (nearly-)acyclic graphs, this problem is known to be solvable in
polynomial time. In this paper, larger classes of tractable instances are
singled out, by discussing solution approaches based on exploiting hypergraph
acyclicity and, more generally, structural decomposition methods, such as
(hyper)tree decompositions
Ride Sharing with a Vehicle of Unlimited Capacity
A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle travels through the graph, carrying each object from its origin to its destination without any bound on the number of objects that can be simultaneously transported. The vehicle starts and terminates its ride at given nodes, and the goal is to compute a minimum-cost ride satisfying all requests. This ride sharing problem is shown to be tractable on paths by designing a O(h*log(h)+n) algorithm, with h being the number of distinct requests and with n being the number of nodes in the path. The algorithm is then used as a subroutine to efficiently solve instances defined over cycles, hence covering all graphs with maximum degree 2. This traces the frontier of tractability, since NP-hard instances are exhibited over trees whose maximum degree is 3
Tree Projections and Structural Decomposition Methods: The Power of Local Consistency and Larger Islands of Tractability
Evaluating conjunctive queries and solving constraint satisfaction problems
are fundamental problems in database theory and artificial intelligence,
respectively. These problems are NP-hard, so that several research efforts have
been made in the literature for identifying tractable classes, known as islands
of tractability, as well as for devising clever heuristics for solving
efficiently real-world instances. Many heuristic approaches are based on
enforcing on the given instance a property called local consistency, where (in
database terms) each tuple in every query atom matches at least one tuple in
every other query atom. Interestingly, it turns out that, for many well-known
classes of queries, such as for the acyclic queries, enforcing local
consistency is even sufficient to solve the given instance correctly. However,
the precise power of such a procedure was unclear, but for some very restricted
cases. The paper provides full answers to the long-standing questions about the
precise power of algorithms based on enforcing local consistency. The classes
of instances where enforcing local consistency turns out to be a correct
query-answering procedure are however not efficiently recognizable. In fact,
the paper finally focuses on certain subclasses defined in terms of the novel
notion of greedy tree projections. These latter classes are shown to be
efficiently recognizable and strictly larger than most islands of tractability
known so far, both in the general case of tree projections and for specific
structural decomposition methods
Group reasoning in social environments
While modeling group decision making scenarios, the existence of a central authority is often assumed which is in charge of amalgamating the preferences of a given set of agents with the aim of
computing a socially desirable outcome, for instance, maximizing
the utilitarian or the egalitarian social welfare. Departing from this
classical perspective and inspired by the growing body of literature
on opinion formation and diffusion, a setting for group decision
making is studied where agents are selfishly interested and where
each of them can adopt her own decision without a central coordination, hence possibly disagreeing with the decision taken by some
of the other agents. In particular, it is assumed that agents belong
to a social environment and that their preferences on the available
alternatives can be influenced by the number of “neighbors” agree-
ing/disagreeing with them. The setting is formalized and studied
by modeling agents’ reasoning capabilities in terms of weighted
propositional logics and by focusing on Nash-stable solutions as the
prototypical solution concept. In particular, a thoroughly computational complexity analysis is conducted on the problem of deciding
the existence of such stable outcomes. Moreover, for the classes
of environments where stability is always guaranteed, the convergence of Nash dynamics consisting of sequences of best response
updates is studied, too
Detecting and repairing anomalous evolutions in noisy environments: logic programming formalization and complexity results
In systems where agents are required to interact with a partially known and dynamic world, sensors can be used to obtain further knowledge about the environment. However, sensors may be unreliable, that is, they may deliver wrong information (due, e.g., to hardware or software malfunctioning) and, consequently, they may cause agents to take wrong decisions, which is a scenario that should be avoided. The paper considers the problem of reasoning in noisy environments in a setting where no (either certain or probabilistic) data is available in advance about the reliability of sensors. Therefore, assuming that each agent is equipped with a background theory (in our setting, an extended logic program) encoding its general knowledge about the world, we define a concept of detecting an anomaly perceived in sensor data and the related concept of agent recovering to a coherent status of information. In this context, the complexities of various anomaly detection and anomaly recovery problems are studied.IFIP International Conference on Artificial Intelligence in Theory and Practice - Agents 1Red de Universidades con Carreras en Informática (RedUNCI
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