http://hdl.handle.net/2117/3094 2013-05-25T17:11:15Z http://hdl.handle.net/2117/12953 Title: On the proper intervalization of colored caterpillar trees Authors: Álvarez Faura, M. del Carme; Serna Iglesias, María José Abstract: This paper studies the computational complexity of the Proper interval colored graph problem (picg), when the input graph is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the picg and a graph layout problem the Proper colored layout problem (pclp). We show a dichotomy: the picg and the pclp are NP-complete for colored caterpillars of hair length ≥ 2, while both problems are in P for colored caterpillars of hair length < 2. For the hardness results we provide a reduction from the Multiprocessor Scheduling problem, while the polynomial time results follow from a characterization in terms of forbidden subgraphs. 2011-07-13T09:48:20Z http://hdl.handle.net/2117/12934 Title: Sensor field: a computational model Authors: Álvarez Faura, M. del Carme; Duch Brown, Amalia; Gabarró Vallès, Joaquim; Serna Iglesias, María José Abstract: We introduce a formal model of computation for networks of tiny artifacts, the static synchronous sensor field model (SSSF) which considers that the devices communicate through a fixed communication graph and interact with the environment through input/output data streams. We analyze the performance of SSSFs solving two sensing problems the Average Monitoring and the Alerting problems. For constant memory SSSFs we show that the set of recognized languages is contained in DSPACE(n+m) where n is the number of nodes of the communication graph and m its number of edges. Finally we explore the capabilities of SSSFs having sensing and additional non-sensing constant memory devices. 2011-07-12T10:23:04Z http://hdl.handle.net/2117/9758 Title: Theoretical aspects of graph models for MANETS Authors: Díaz Cort, Josep; Dieter Wilhelm, Mitsche; Santi, Paolo Abstract: We survey the main theoretical aspects of models for Mobile Ad Hoc Networks (MANETs). We present theoretical characterizations of mobile network structural properties, di erent dynamic graph models of MANETs, and nally we give detailed summaries of a few selected articles. In particular, we focus on articles dealing with connectivity of mobile networks, and on articles which show that mobility can be used to propagate information between nodes of the network while at the same time maintaining small transmission distances, and thus saving energy. 2010-10-18T10:04:10Z http://hdl.handle.net/2117/9550 Title: Maximum tolerance and maximum greatest tolerance Authors: Freixas Bosch, Josep; Molinero Albareda, Xavier Abstract: An important consideration when applying neural networks is the sensitivity to weights and threshold in strict separating systems representing a linearly separable function. Two parameters have been introduced to measure the relative errors in weights and threshold of strict separating systems: the tolerance and the greatest tolerance. Given an arbitrary separating system we study which is the equivalent separating system that provides maximum tolerance or/and maximum greatest tolerance. 2010-10-07T14:19:24Z http://hdl.handle.net/2117/9295 Title: Weighted games without a unique minimal representation in integers Authors: Freixas Bosch, Josep; Molinero Albareda, Xavier Abstract: Recerca de jocs amb mínim número de jugadors sense representacions enteres mínimes o mínimes normalitzades Description: Isbell in 1959 was the first to find a weighted game without a minimum integer realization in which the affected players do not play a symmetric role in the game. His example has 12 players is a weighted decisive game, i.e. a weighted game for which a coalition wins iff its complement loses. The goal of this paper is to provide a procedure for weighted games that allows finding out what is the minimum number of players needed to get a weighted game without a minimum integer weighted representation in which the affected players do not play a symmetric role in the game. We prove, by means of an algorithm, that the minimum number of voters required is 9. 2010-10-04T17:23:00Z http://hdl.handle.net/2117/8956 Title: On the complexity of problems on simple games Authors: Freixas Bosch, Josep; Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José Abstract: Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes–no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand, each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation used as input. We consider four natural explicit representations: winning, losing, minimal winning, and maximal losing. We first analyze the complexity of testing whether a game is simple and testing whether a game is weighted. We show that, for the four types of representations, both problems can be solved in polynomial time. Finally, we provide results on the complexity of testing whether a simple game or a weighted game is of a special type. We analyze strongness, properness, decisiveness and homogeneity, which are desirable properties to be fulfilled for a simple game. We finalize with some considerations on the possibility of representing a game in a more succinct representation showing a natural representation in which the recognition problem is hard. 2010-09-17T15:45:57Z http://hdl.handle.net/2117/7703 Title: A Fibonacci sequence for linear structures with two types of components Authors: Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador Abstract: We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to count, up to isomorphism, the number of these voting systems for an arbitrary number of voters. We obtain a closed formula for the number of these systems, this formula follows a Fibonacci sequence with a smooth polynomial variation on the number of voters. 2010-06-16T15:23:20Z