Randomized parallel approximations to max flow

The final publication is available at link.springer.comPeer ReviewedPostprint (author's final draft

Parallel algorithms for two processors precedence constraint scheduling

The final publication is available at link.springer.comPeer ReviewedPostprint (author's final draft

On parallel versus sequential approximation

In this paper we deal with the class NCX of NP Optimization problems that are approximable within constant ratio in NC. This class is the parallel counterpart of the class APX. Our main motivation here is to reduce the study of sequential and parallel approximability to the same framework. To this aim, we first introduce a new kind of NC-reduction that preserves the relative error of the approximate solutions and show that the class NCX has {em complete} problems under this reducibility. An important subset of NCX is the class MAXSNP, we show that MAXSNP-complete problems have a threshold on the parallel approximation ratio that is, there are positive constants $epsilon_1$, $epsilon_2$ such that although the problem can be approximated in P within $epsilon_1$ it cannot be approximated in NC within epsilon_2$, unless P=NC. This result is attained by showing that the problem of approximating the value obtained through a non-oblivious local search algorithm is P-complete, for some values of the approximation ratio. Finally, we show that approximating through non-oblivious local search is in average NC.Postprint (published version

The parallel approximability of a subclass of quadratic programming

In this paper we deal with the parallel approximability of a special class of Quadratic Programming (QP), called Smooth Positive Quadratic Programming. This subclass of QP is obtained by imposing restrictions on the coefficients of the QP instance. The Smoothness condition restricts the magnitudes of the coefficients while the positiveness requires that all the coefficients be non-negative. Interestingly, even with these restrictions several combinatorial problems can be modeled by Smooth QP. We show NC Approximation Schemes for the instances of Smooth Positive QP. This is done by reducing the instance of QP to an instance of Positive Linear Programming, finding in NC an approximate fractional solution to the obtained program, and then rounding the fractional solution to an integer approximate solution for the original problem. Then we show how to extend the result for positive instances of bounded degree to Smooth Integer Programming problems. Finally, we formulate several important combinatorial problems as Positive Quadratic Programs (or Positive Integer Programs) in packing/covering form and show that the techniques presented can be used to obtain NC Approximation Schemes for "dense" instances of such problems.Peer ReviewedPostprint (published version

Web apps and imprecise probabilities

We propose a model for the behaviour of Web apps in the unreliable WWW. Web apps are described by orchestrations. An orchestration mimics the personal use of the Web by defining the way in which Web services are invoked. The WWW is unreliable as poorly maintained Web sites are prone to fail. We model this source of unreliability trough a probabilistic approach. We assume that each site has a probability to fail. Another source of uncertainty is the traffic congestion. This can be observed as a non-deterministic behaviour induced by the variability in the response times. We model non-determinism by imprecise probabilities. We develop here an ex-ante normal to characterize the behaviour of finite orchestrations in the unreliable Web. We show the existence of a normal form under such semantics for orchestrations using asymmetric parallelism.Peer ReviewedPostprint (author's final draft

Measuring satisfaction in societies with opinion leaders and mediators

An opinion leader-follower model (OLF) is a two-action collective decision-making model for societies, in which three kinds of actors are considered:Preprin

Cooperation through social influence

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.Peer ReviewedPostprint (author’s final draft

The complexity of measuring power in generalized opinion leader decision models

We analyze the computational complexity of the power measure in models of collective decision: the generalized opinion leader-follower model and the oblivious and non-oblivious infuence models. We show that computing the power measure is #P-hard in all these models, and provide two subfamilies in which the power measure can be computed in polynomial time.Peer ReviewedPostprint (author's final draft

Uncertainty in basic short-term macroeconomic models with angel-daemon games

We propose the use of an angel-daemon framework to perform an uncertainty analysis of short-term macroeconomic models. The angel-daemon framework defines a strategic game where two agents, the angel and the daemon, act selfishly. These games are defined over an uncertainty profile which presents a short and macroscopic description of a perturbed situation. The Nash equilibria on these games provide stable strategies in perturbed situations, giving a natural estimation of uncertainty. We apply the framework to the uncertainty analysis of linear versions of the IS-LM and the IS-MP models.Peer ReviewedPostprint (author's final draft

Finite memory devices in CSP

It is often said that a state based approach to CSP is inadequate, however we present here some (theoretical) hints against this assertion. A new class of processes modelled by finite memory devices are considered. These devices (called here CSP automata) allow both: deal with the different kinds of nondeterminism at a state level and model misbehaviours due to divergences. They are well adapted to the semantics of failures plus divergences. As CSP is independent of branching time CSP-automata can be determinized. Furthermore we show that an extension of the classical automata's morphism is equivalent to refinement between processes. That allow us to define canonical forms through minimization. These processes can also be characterized by a set of recursive equations so called linear systems. These processes are stable under nondeterminism, change of symbol, prefixing and interleaving.Postprint (published version