First-Fit is Linear on Posets Excluding Two Long Incomparable Chains

A poset is (r + s)-free if it does not contain two incomparable chains of size r and s, respectively. We prove that when r and s are at least 2, the First-Fit algorithm partitions every (r + s)-free poset P into at most 8(r-1)(s-1)w chains, where w is the width of P. This solves an open problem of Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992--1999, 2010).Comment: v3: fixed some typo

A Characterization of Mixed Unit Interval Graphs

We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half-open unit intervals of the real line. This is a proper superclass of the well known unit interval graphs. Our result solves a problem posed by Dourado, Le, Protti, Rautenbach and Szwarcfiter (Mixed unit interval graphs, Discrete Math. 312, 3357-3363 (2012)).Comment: 17 pages, referees' comments adde

The Queue-Number of Posets of Bounded Width or Height

Heath and Pemmaraju conjectured that the queue-number of a poset is bounded by its width and if the poset is planar then also by its height. We show that there are planar posets whose queue-number is larger than their height, refuting the second conjecture. On the other hand, we show that any poset of width $2$ has queue-number at most $2$, thus confirming the first conjecture in the first non-trivial case. Moreover, we improve the previously best known bounds and show that planar posets of width $w$ have queue-number at most $3w-2$ while any planar poset with $0$ and $1$ has queue-number at most its width.Comment: 14 pages, 10 figures, Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Transformations structurelles et essor du métal

The role of multiattribute utility theory is first placed in the overall context of decision analysis. Then an approach that has proven useful in adapting the theory to be a practical tool is illustrated. Several cases where multiattribute utility has been used are briefly discussed. These include both operational and strategic problems involving, for example, siting of large-scale facilities (airports, power plants), medical treatment, the structuring corporate objectives, environmental management, and personal investment strategy

Mean-risk models using two risk measures: A multi-objective approach

This paper proposes a model for portfolio optimisation, in which distributions are characterised and compared on the basis of three statistics: the expected value, the variance and the CVaR at a specified confidence level. The problem is multi-objective and transformed into a single objective problem in which variance is minimised while constraints are imposed on the expected value and CVaR. In the case of discrete random variables, the problem is a quadratic program. The mean-variance (mean-CVaR) efficient solutions that are not dominated with respect to CVaR (variance) are particular efficient solutions of the proposed model. In addition, the model has efficient solutions that are discarded by both mean-variance and mean-CVaR models, although they may improve the return distribution. The model is tested on real data drawn from the FTSE 100 index. An analysis of the return distribution of the chosen portfolios is presented

A Self Healing Microservices Architecture: A Case Study in Docker Swarm Cluster

One desired aspect of a self-adapting microservices architecture is the ability to continuously monitor the operational environment, detect and observe anomalous behaviour as well as implement a reasonable policy for self-scaling, self-healing, and self-tuning the computational resources in order to dynamically respond to a sudden change in its operational environment. Often the behaviour of a microservices architecture continuously changes over time and the identification of both normal and abnormal behaviours of running services becomes a challenging task. This paper proposes a self-healing Microservice architecture that continuously monitors the operational environment, detects and observes anomalous behaviours, and provides a reasonable adaptation policy using a multi-dimensional utility-based model. This model preserves the cluster state and prevents multiple actions to taking place at the same time. It also guarantees that the executed adaptation action fits the current execution context and achieves the adaptation goals. The results show the ability of this model to dynamically scale the architecture horizontally or vertically in response to the context changes

Recognizing Members of the Tournament Equilibrium Set is NP-hard

A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given a binary dominance relation on a set of alternatives. Schwartz's tournament equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context. Due to its unwieldy recursive definition, little is known about TEQ. In particular, its monotonicity remains an open problem up to date. Yet, if TEQ were to satisfy monotonicity, it would be a very attractive tournament solution concept refining both the Banks set and Dutta's minimal covering set. We show that the problem of deciding whether a given alternative is contained in TEQ is NP-hard.Comment: 9 pages, 3 figure

Penalty-Based Aggregation of Strings

International Summer School on Aggregation Operators (2019. Olomouc, Czech Republic