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

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views, whose solutions are either already available or can be computed efficiently. The goal is to arrange portions of these views in a tree-like structure, called tree projection, which determines an efficiently solvable CSP instance equivalent to the original one. Deciding whether a tree projection exists is NP-hard. Solution methods have therefore been proposed in the literature that do not require a tree projection to be given, and that either correctly decide whether the given CSP instance is satisfiable, or return that a tree projection actually does not exist. These approaches had not been generalized so far on CSP extensions for optimization problems, where the goal is to compute a solution of maximum value/minimum cost. The paper fills the gap, by exhibiting a fixed-parameter polynomial-time algorithm that either disproves the existence of tree projections or computes an optimal solution, with the parameter being the size of the expression of the objective function to be optimized over all possible solutions (and not the size of the whole constraint formula, used in related works). Tractability results are also established for the problem of returning the best K solutions. Finally, parallel algorithms for such optimization problems are proposed and analyzed. Given that the classes of acyclic hypergraphs, hypergraphs of bounded treewidth, and hypergraphs of bounded generalized hypertree width are all covered as special cases of the tree projection framework, the results in this paper directly apply to these classes. These classes are extensively considered in the CSP setting, as well as in conjunctive database query evaluation and optimization

Wood pellet as biofuel: a life cycle analysis of a domestic and industrial production chain

This study focuses on the environmental impact assessment through Life Cycle Assessment (LCA). In particular, the aims are to compare the environmental impacts of ‘‘A1 premium’’ wood pellet manufacturing in a large industrial plant with “domestic” wood pellet manufacturing in a small pelletiser, and to identify the environmental hotspots of these two pellet productive chains. The raw material, for both systems is maritime pine wood. A cradle-to grave life-cycle inventory is used and, thus, the system boundary began with the forest stage and ended with ashes disposal after pellet burning. For the forest stage, two scenarios were simulated (intensive and extensive). Moreover, in a sensitivity analysis, alternative scenarios were tested for pellet burning (higher and lower emissions) and for transports (higher distances). The results underline that electricity consumption due to machinery used for the compressing phases of pelletising process has a key role in the environmental profile, together with pellet burning. The production of the wood has a low impact if compared with the other main stages of the pellet production chain. The sensitivity analysis revealed that transport distances have a great impact in the ozone depletion category and climate change, especially when a high transport distance is assumed. Moreover the sensitivity analysis demonstrated that the pellet burning stage has a large impact, even when low emissions are adopted. The industrial model, with high emissions assumed for pellet burning is the worst scenario in terms of environmental performance. The model with less overall environmental impacts is the domestic model, with low emissions for pellet burning and extensive forest management. The comparison between the domestic and industrial model shows that, the domestic model performs better, having better performances on 6 impact categories out of 8

Monomer and polymer indole-derived systems having NLO properties for very high optical gain photorefractive materials. The role of the electrostatic interactions.

Object of the present research is the study of some indole-based photorefractive (PR) materials. Novel indole-based NLO chromophores have been synthesized and their photoconductive (PC) and PR behaviour have been investigated when employed both alone (as low molecular weight glass forming multifunctional PR moieties) as well as in blends with a PC indolyl polymer, namely poly-(N-vinyl-2,3-dimethylindole). The aim was to get more insight in the onset of PR effect and to evaluate various contributions to it related to intermolecular interactions occurring among the components of a PR material. The introduction of increasing contents of polymer counterpart in PR blends containing the novel NLO chromophores permitted to follow these interactions in their onset and the establishment of new supramolecular arrangements, expected to be responsible for dramatic changes of electrooptic properties. In this way, it has been also possible to look for the proper formulation in order to take advantage of such interactions for the achievement of the best PC and PR performances. The joint analysis of the results of PC, PR and thermal (DSC) behaviour of the investigated materials revealed itself as particularly useful, due to the complexity of the many processes occurring simultaneously in organic PR materials. A careful comparison with numerous theoretical treatments permitted to rationalize the obtained results and to put in evidence the prominent role played by intermolecular interactions. On the other hand, the obtaining of long-term phase stability of amorphous PR materials, desirable for their practical use in a number of applications, was also a challenge. Many PR materials described in the past, indeed, although having good photorefractive properties, showed the undesirable drawback of fast recrystallization of one or more of their molecular components, leading to opacization of films and to the rapid loss of PR properties. Such aspect has been faced during this research obtaining indefinitely stable materials. As concerns PR, very large values of the photorefractive optical gain Γ (a main PR figure of merit) have been achieved in many cases, classifying the materials object of this research among the most efficient PR materials