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Abstract: There are many folded states consistent with a given mountain–valley pattern of equidistant creases on a long paper strip. We would like to fold a paper strip such that the number of paper layers between each pair of hinged paper segments, called the crease width at the crease point, is minimized. This problem is called the stamp folding problem and there are two variants of this problem: minimization of the maximum crease width, and minimization of the total crease width. This optimization problem was recently introduced and investigated from the viewpoint of the counting problem. However, its computational complexity is not known. In this paper, we first show that the minimization problem of the maximum crease width is strongly NP-complete. Hence we cannot solve the problem in polynomial time unless P=NP. We next propose an algorithm that solves the minimization problem. The algorithm itself is a straightforward one, but its analysis is not trivial. We show that this algorithm runs in time where is the number of creases and is the total crease width. [Copyright &y& Elsevier]

Abstract: Much of the literature on multi-agent coalition formation has focused on Characteristic Function Games, where the effectiveness of a coalition is not affected by how the other agents are arranged in the system. In contrast, very little attention has been given to the more general class of Partition Function Games, where the emphasis is on how the formation of one coalition could influence the performance of other co-existing coalitions in the system. However, these inter-coalitional dependencies, called externalities from coalition formation, play a crucial role in many real-world multi-agent applications where agents have either conflicting or overlapping goals. Against this background, this paper is the first computational study of coalitional games with externalities in the multi-agent system context. We focus on the Coalition Structure Generation (CSG) problem which involves finding an exhaustive and disjoint division of the agents into coalitions such that the performance of the entire system is optimized. While this problem is already very challenging in the absence of externalities, due to the exponential size of the search space, taking externalities into consideration makes it even more challenging as the size of the input, given n agents, grows from to . Our main contribution is the development of the first CSG algorithm for coalitional games with either positive or negative externalities. Specifically, we prove that it is possible to compute upper and lower bounds on the values of any set of disjoint coalitions. Building upon this, we prove that in order to establish a worst-case guarantee on solution quality it is necessary to search a certain set of coalition structures (which we define). We also show how to progressively improve this guarantee with further search. Since there are no previous CSG algorithms for games with externalities, we benchmark our algorithm against other state-of-the-art approaches in games where no externalities are present. Surprisingly, we find that, as far as worst-case guarantees are concerned, our algorithm outperforms the others by orders of magnitude. For instance, to reach a bound of 3 given 24 agents, the number of coalition structures that need to be searched by our algorithm is only 0.0007% of that needed by Sandholm et al. (1999) , and 0.5% of that needed by Dang and Jennings (2004) . This is despite the fact that the other algorithms take advantage of the special properties of games with no externalities, while ours does not. [Copyright &y& Elsevier]

Abstract: This paper proposes a probability formulation that unifies both single-image deblurring and multi-image denoising using variational inference. The proposed formulation is based on a theoretical analysis that compares denoising and deblurring in the same probabilistic framework, and supported by a practical approach that deal with general motion that creates HDR images in the presence of spatially varying motion. Based on this formulation, a new algorithm for deblurring a noisy and blurry image pair is presented. Besides, we provide also an approach that combines existing optical flow and image denoising techniques for High Dynamic Range imaging. [Copyright &y& Elsevier]

Abstract: Several methods have been developed to construct -free automata that represent a regular expression. Among the most widely known are the position automaton (Glushkov), the partial derivatives automaton (Antimirov) and the follow automaton (Ilie and Yu). All these automata can be obtained with quadratic time complexity, thus, the comparison criterion is usually the size of the resulting automaton. The methods that obtain the smallest automata (although, for general expressions, they are not comparable), are the follow and the partial derivatives methods. In this paper, we propose another method to obtain a -free automaton from a regular expression. The number of states of the automata we obtain is bounded above by the size of both the partial derivatives automaton and of the follow automaton. Our algorithm also runs with the same time complexity of these methods. [Copyright &y& Elsevier]

Abstract: Given a graph in which a fugitive hides on vertices or along edges, graph searching problems are usually to find the minimum number of searchers required to capture the fugitive. In this paper, we consider the problem of finding the minimum number of steps to capture the fugitive. We introduce the fast edge searching problem in the edge search model, which is the problem of finding the minimum number of steps (called the fast edge-search time) to capture the fugitive. We establish relations between the fast edge searching and the fast searching that is the problem of finding the minimum number of searchers to capture the fugitive in the fast search model. While the family of graphs whose fast search number is at most is not minor-closed for any positive integer , we show that the family of graphs whose fast edge-search time is at most is minor-closed. We establish relations between the fast (fast edge) searching and the node searching. These relations allow us to transform the problem of computing node search numbers to the problem of computing fast edge-search numbers or fast search numbers. Using these relations, we prove that the problem of deciding, given a graph and an integer , whether the fast (edge-)search number of is less than or equal to is NP-complete; and it remains NP-complete for Eulerian graphs. We also prove that the problem of determining whether the fast (edge-)search number of is half of the number of odd vertices in is NP-complete; and it remains NP-complete for planar graphs with maximum degree 4. We present a linear time approximation algorithm for the fast edge-search time that always delivers solutions of at most times the optimal value. This algorithm also gives us a tight upper bound on the fast search number of graphs. We also show a lower bound on the fast search number using the minimum degree and the number of odd vertices. [Copyright &y& Elsevier]