Let I be an instance of the stable marriage (SM) problem. In the late 1990s, Teo and Sethuraman discovered the existence of median stable matchings, which are stable matchings that match all participants to their (lower/upper) median stable partner. About a decade later, Cheng showed that not only are they locally-fair, but they are also globally-fair in the following sense: when G(I) is the co...

This paper addresses strategies for the stable roommates problem, assuming that a stable matching is chosen at random. We investigate how a cheating man should permute his preference list so that he has a higher-ranking roommate probabilistically. In the first part of the paper, we identify a necessary condition for creating a new stable roommate for the cheating man. This condition precludes a...

We propose a proof-theoretical way of obtaining detailed and precise information on conceptual hierarchies. The notion of concept finding proof, which represents a hierarchy of concepts, is introduced based on a substructural logic with mingle and strong negation. Mingle, which is a structural inference rule, is used to represent a process for finding a more general (or specific) concept than s...

For a general logic program, a set of n+ 1 logic values is considered and an unde ned value denoted u. Partial multi-valued interpretations are also de ned. A general logic program P may contain the constants that are de ned for every logic value. A pseudo-negation denoted eh is de ned for every integer h, where 0 h < n. A partial ordering denoted h is de ned between multi-valued interpretation...

Matching games form a class of coalitional games that attracted much attention in the literature. Indeed, several results are known about the complexity of computing over them solution concepts. In particular, it is known that computing the Shapley value is intractable in general, formally #P-hard, and feasible in polynomial time over games defined on trees. In fact, it was an open problem whet...

Allocation games are coalitional games defined in the literature as a way to analyze fair division problems of indivisible goods. The prototypical solution concepts for them are the Shapley value and the Banzhaf value. Unfortunately, their computation is intractable, formally #P-hard. Motivated by this bad news, structural requirements are investigated which can be used to identify islands of t...

In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money compensation to perform a fair allocation taking into account the actual contribution of all agents to the social welfare. Coalitional games provide a formal mathema...

Unitary representations of the fundamental group of a Kähl-er manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to poly-stable Higgs bundles. In this paper we find the objects corresponding to affine representations: the linear part gives a Higgs bundle and the translation part corresponds to an element of a generalized...

In this paper we investigate the parallel complexity of computing the stable model of acyclic general logic programs Within this class of logic programs we consider the cases of negative and de nite logic programs Both cases are proved to be P complete We prove the same for a related problem namely that of computing the kernel of a directed acyclic graph

In this paper we review some theoretical results about the p-stable semantics, and based on that, we design some algorithms that search for the p-stable models of a normal program. An important point is that some of these algorithms can also be used to compute the stratified minimal models of a normal program.