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On the complexity of problems on simple games

Josep Freixas, Xavier Molinero, Martin Olsen, Maria Serna (2011)

RAIRO - Operations Research - Recherche Opérationnelle

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...

On the complexity of problems on simple games

Josep Freixas, Xavier Molinero, Martin Olsen, Maria Serna (2012)

RAIRO - Operations Research

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....

On the complexity of the Shapley-Scarf economy with several types of goods

Katarína Cechlárová (2009)

Kybernetika

In the Shapley-Scarf economy each agent is endowed with one unit of an indivisible good (house) and wants to exchange it for another, possibly the most preferred one among the houses in the market. In this economy, core is always nonempty and a core allocation can be found by the famous Top Trading Cycles algorithm. Recently, a modification of this economy, containing Q >= 2 types of goods (say, houses and cars for Q=2) has been introduced. We show that if the number of agents is 2, a complete...

On the computational complexity of centers locating in a graph

Ján Plesník (1980)

Aplikace matematiky

It is shown that the problem of finding a minimum k -basis, the n -center problem, and the p -median problem are N P -complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal m -center problem is also N P -complete.

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