Specializations and Generalizations of the Stackelberg Minimum Spanning Tree Game

Let be given a graph $G=(V,E)$ whose edge set is partitioned into a set $R$ of \emph{red} edges and a set $B$ of \emph{blue} edges, and assume that red edges are weighted and form a spanning tree of $G$. Then, the \emph{Stackelberg Minimum Spanning Tree} (\stack) problem is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized. \stack \ is known to be \apx-hard already when the number of distinct red weights is 2. In this paper we analyze some meaningful specializations and generalizations of \stack, which shed some more light on the computational complexity of the problem. More precisely, we first show that if $G$ is restricted to be \emph{complete}, then the following holds: (i) if there are only 2 distinct red weights, then the problem can be solved optimally (this contrasts with the corresponding \apx-hardness of the general problem); (ii) otherwise, the problem can be approximated within $7/4 + \epsilon$, for any $\epsilon > 0$. Afterwards, we define a natural extension of \stack, namely that in which blue edges have a non-negative \emph{activation cost} associated, and it is given a global \emph{activation budget} that must not be exceeded when pricing blue edges. Here, after showing that the very same approximation ratio as that of the original problem can be achieved, we prove that if the spanning tree of red edges can be rooted so as that any root-leaf path contains at most $h$ edges, then the problem admits a $(2h+\epsilon)$-approximation algorithm, for any $\epsilon > 0$.Comment: 22 pages, 7 figure

Computational comparisons of different formulations for the Bilevel Minimum Spanning Tree Problem

International audienceLet be given a graph G = (V, E) whose edge set is partitioned into a set R of red edges and a set B of blue edges, and assume that red edges are weighted and contain a spanning tree of G. Then, the Bilevel Minimum Spanning Tree Problem (BMSTP) is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized. In this paper we present different mathematical formulations for the BMSTP based on the properties of the Minimum Spanning Tree Problem and the bilevel optimization. We establish a theoretical and empirical comparison between these new formulations and we also provide reinforcements that together with a proper formulation are able to solve medium to big size instances random instances. We also test our models in instances already existing in the literature

Multi-Agent Systems

A multi-agent system (MAS) is a system composed of multiple interacting intelligent agents. Multi-agent systems can be used to solve problems which are difficult or impossible for an individual agent or monolithic system to solve. Agent systems are open and extensible systems that allow for the deployment of autonomous and proactive software components. Multi-agent systems have been brought up and used in several application domains

Specializations and Generalizations of the Stackelberg Minimum Spanning Tree Game

The Stackelberg Minimum Spanning Tree (StackMST) game is a network pricing (bilevel) optimization problem. The game is played by two players on a graph G = (V,E), whose edges are partitioned into two sets: a set R of red edges (inducing a spanning tree of G) with a fixed non-negative real cost, and a set B of blue edges which are instead priced by a leader. This is done with the final intent of maximizing a revenue that will be returned for their purchase by a follower, whose goal in turn is to select a minimum spanning tree of G. StackMST is known to be APX-hard already when the number of distinct red costs is 2, as well as min {k, 1 + ln β, 1 + ln ρ}-approximable, where k is the number of distinct red costs, β is the number of blue edges selected by the follower in an optimal pricing, and ρ is the maximum ratio between red costs. In this paper we analyze some meaningful specializations and generalizations of StackMST, which shed some more light on the computational complexity of the game. More precisely, we first show that if G is complete, then the following holds: (i) if there are only 2 distinct red costs, then the problem can be solved optimally (this contrasts with the corresponding APX-hardness of the general problem); (ii) otherwise, the problem can be approximated within 7/4 + ε, for any ε> 0. Afterwards, we define a natural extension of StackMST, namely that in which blue edges have a non-negative activation cost associated, and the leader has a global activation budget that must not be exceeded, and, after showing that the very same approximation ratio as that of the original game can be achieved, we prove that if the spanning tree induced by the red edges has radius h (in terms of number of edges), then the problem admits a (2h + ε)-approximation algorithm

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

Augmentation of Brain Function: Facts, Fiction and Controversy. Volume III: From Clinical Applications to Ethical Issues and Futuristic Ideas

The final volume in this tripartite series on Brain Augmentation is entitled “From Clinical Applications to Ethical Issues and Futuristic Ideas”. Many of the articles within this volume deal with translational efforts taking the results of experiments on laboratory animals and applying them to humans. In many cases, these interventions are intended to help people with disabilities in such a way so as to either restore or extend brain function. Traditionally, therapies in brain augmentation have included electrical and pharmacological techniques. In contrast, some of the techniques discussed in this volume add specificity by targeting select neural populations. This approach opens the door to where and how to promote the best interventions. Along the way, results have empowered the medical profession by expanding their understanding of brain function. Articles in this volume relate novel clinical solutions for a host of neurological and psychiatric conditions such as stroke, Parkinson’s disease, Huntington’s disease, epilepsy, dementia, Alzheimer’s disease, autism spectrum disorders (ASD), traumatic brain injury, and disorders of consciousness. In disease, symptoms and signs denote a departure from normal function. Brain augmentation has now been used to target both the core symptoms that provide specificity in the diagnosis of a disease, as well as other constitutional symptoms that may greatly handicap the individual. The volume provides a report on the use of repetitive transcranial magnetic stimulation (rTMS) in ASD with reported improvements of core deficits (i.e., executive functions). TMS in this regard departs from the present-day trend towards symptomatic treatment that leaves unaltered the root cause of the condition. In diseases, such as schizophrenia, brain augmentation approaches hold promise to avoid lengthy pharmacological interventions that are usually riddled with side effects or those with limiting returns as in the case of Parkinson’s disease. Brain stimulation can also be used to treat auditory verbal hallucination, visuospatial (hemispatial) neglect, and pain in patients suffering from multiple sclerosis. The brain acts as a telecommunication transceiver wherein different bandwidth of frequencies (brainwave oscillations) transmit information. Their baseline levels correlate with certain behavioral states. The proper integration of brain oscillations provides for the phenomenon of binding and central coherence. Brain augmentation may foster the normalization of brain oscillations in nervous system disorders. These techniques hold the promise of being applied remotely (under the supervision of medical personnel), thus overcoming the obstacle of travel in order to obtain healthcare. At present, traditional thinking would argue the possibility of synergism among different modalities of brain augmentation as a way of increasing their overall effectiveness and improving therapeutic selectivity. Thinking outside of the box would also provide for the implementation of brain-to-brain interfaces where techniques, proper to artificial intelligence, could allow us to surpass the limits of natural selection or enable communications between several individual brains sharing memories, or even a global brain capable of self-organization. Not all brains are created equal. Brain stimulation studies suggest large individual variability in response that may affect overall recovery/treatment, or modify desired effects of a given intervention. The subject’s age, gender, hormonal levels may affect an individual’s cortical excitability. In addition, this volume discusses the role of social interactions in the operations of augmenting technologies. Finally, augmenting methods could be applied to modulate consciousness, even though its neural mechanisms are poorly understood. Finally, this volume should be taken as a debate on social, moral and ethical issues on neurotechnologies. Brain enhancement may transform the individual into someone or something else. These techniques bypass the usual routes of accommodation to environmental exigencies that exalted our personal fortitude: learning, exercising, and diet. This will allow humans to preselect desired characteristics and realize consequent rewards without having to overcome adversity through more laborious means. The concern is that humans may be playing God, and the possibility of an expanding gap in social equity where brain enhancements may be selectively available to the wealthier individuals. These issues are discussed by a number of articles in this volume. Also discussed are the relationship between the diminishment and enhancement following the application of brain-augmenting technologies, the problem of “mind control” with BMI technologies, free will the duty to use cognitive enhancers in high-responsibility professions, determining the population of people in need of brain enhancement, informed public policy, cognitive biases, and the hype caused by the development of brain- augmenting approaches