Phase Transitions of the Typical Algorithmic Complexity of the Random Satisfiability Problem Studied with Linear Programming

Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in polynomial time for suitable ranges of the parameter. In fact, random $K$-SAT, with $\alpha=M/N$ as control parameter, can be solved quickly for small enough values of $\alpha$. It shows a phase transition between a satisfiable phase and an unsatisfiable phase. For branch and bound algorithms, which operate in the space of feasible Boolean configurations, the empirically hardest problems are located only close to this phase transition. Here we study $K$-SAT ($K=3,4$) and the related optimization problem MAX-SAT by a linear programming approach, which is widely used for practical problems and allows for polynomial run time. In contrast to branch and bound it operates outside the space of feasible configurations. On the other hand, finding a solution within polynomial time is not guaranteed. We investigated several variants like including artificial objective functions, so called cutting-plane approaches, and a mapping to the NP-complete vertex-cover problem. We observed several easy-hard transitions, from where the problems are typically solvable (in polynomial time) using the given algorithms, respectively, to where they are not solvable in polynomial time. For the related vertex-cover problem on random graphs these easy-hard transitions can be identified with structural properties of the graphs, like percolation transitions. For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions. This renders the behaviour of random $K$-SAT more complex than, e.g., the vertex-cover problem.Comment: 11 pages, 5 figure

Energy landscapes of some matching-problem ensembles

The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy landscape of different ensembles. Erd\"os-Renyi graphs and ring graphs with randomly added edges are considered and two types of distributions for the random edge weighs are used. For maximum-weight matching, fast and scalable algorithms exist, such that we can study large graphs of more than $10^5$ nodes. Our results show that the structure of the energy landscape for standard ensembles of matching is simple, comparable to the energy landscape of a ferromagnet. Nonetheless, for some of the here presented ensembles our results allow for the presence of complex energy landscapes in the spirit of Replica-Symmetry Breaking.Comment: 9 pages, 5 figure

Hybrid meta-heuristics for combinatorial optimization

Combinatorial optimization problems arise, in many forms, in vari- ous aspects of everyday life. Nowadays, a lot of services are driven by optimization algorithms, enabling us to make the best use of the available resources while guaranteeing a level of service. Ex- amples of such services are public transportation, goods delivery, university time-tabling, and patient scheduling. Thanks also to the open data movement, a lot of usage data about public and private services is accessible today, sometimes in aggregate form, to everyone. Examples of such data are traffic information (Google), bike sharing systems usage (CitiBike NYC), location services, etc. The availability of all this body of data allows us to better understand how people interacts with these services. However, in order for this information to be useful, it is necessary to develop tools to extract knowledge from it and to drive better decisions. In this context, optimization is a powerful tool, which can be used to improve the way the available resources are used, avoid squandering, and improve the sustainability of services. The fields of meta-heuristics, artificial intelligence, and oper- ations research, have been tackling many of these problems for years, without much interaction. However, in the last few years, such communities have started looking at each other’s advance- ments, in order to develop optimization techniques that are faster, more robust, and easier to maintain. This effort gave birth to the fertile field of hybrid meta-heuristics.openDottorato di ricerca in Ingegneria industriale e dell'informazioneopenUrli, Tommas

The impact of commercial and artistic photography on the portrayal of reality

This report discusses the impact of commercial and artistic photography on the portrayal of reality. It is based on my six-month experience as an intern at Atelier Mai 98 in Paris, a studio devoted to the production of pictures for the luxury market. In my reflection I intend to demonstrate the close bonds between photography and the advertising industry as far as its conception, distribution and aestheticization are concerned. My aim is to discuss how commercial photography creates codes that modify the perception of reality for commercial reasons whereas artistic photography designs an alternative world by revealing the invisible

Quantum Annealing: Research and Applications

This thesis studies several aspects of the quantum annealing (QA) computing approach. Quantum annealers' primary objective is to solve hard computational optimization problems. Because these optimization problems are in the NP-Hard complexity class, they are of great interest in several fields. One of the leading open questions concerning quantum annealers asks whether they will outperform other classical methods for solving these problems; Some aspects of this question are addressed in this thesis. The first part of the thesis investigates whether quantum annealing provides improved performance for solving a particular family of NP problems, called the Quadratic Knapsack Problem (QKP), using the D-Wave Quantum Annealer. The performance metrics used to assess QKP solving are the solution quality and the total runtime, and are benchmarked against other classical solvers. Furthermore, we extend our research on quantum annealers to propose two use cases for such systems. One is for Blockchain technology, and the second is in the area of quantum chaos. For the first use case of QA, an application for Blockchain's Proof of Work (PoW) is proposed, based on having hard optimization problems as an alternative to PoW hashing challenge, and using quantum annealers as solvers. For the second use case of QA, we propose simulating quantum chaos on the D-Wave Quantum Annealer to study the transition between the deep quantum realm and the classical limit in a chaotic system, and obtain insights into the “quantumness" of quantum annealers

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Development and application of a genetic algorithm-informational modeling approach to exploatory statistical modeling of lizard-habitat relationships

Anolis carolinensis, an arboreal lizard common to the southeasternUnited States, has been studied often in lab settings, but infrequently in its natural habitats with respect to the ecology of this species. The current study conducted exploratory statistical modeling of associations between 18 habitat features and the occurrence of A. carolinensis in study plots at the northern distributional limits of this species in eastern Tennessee.Statistical hypothesis-testing procedures and stepwise computer algorithms are commonly used by ecologists to analyze observational (nonexperimental)multivariate data, such as the data analyzed in this study.However, such procedures and algorithms are frequently, but inappropriately, used to find the single supposedly \u27best statistical models and/or support interpretations of the importance or causal nature of variables in the model. Thus, such analyses provide only a narrow scientific view of the multivariate data and the many potentially useful models.The present study developed a genetic algorithm-information modeling (GAIM) approach to a) reduce certain computational and statistical limitations imposed by stepwise algorithms and hypothesis testing procedures, respectively, and b) conduct a wider exploration of any observational multivariate data set. The GAIM approach utilizes a genetic algorithm, which bases its searching power on biological and evolutionary concepts, and the informational approach to statistics, which bases its ability to rank and evaluate models on statistical likelihood and information theory. It is suggested that researchers use an approach that provides a wider view of the data (e.g., finds many models that fit the datawell instead of just one or a few models), such as the GAIM approach, to more fully explore observational multivariate data. The set of well-fitting models obtained from a GAIM analysis can then be used to propose combinations of variables or factors that could be investigated by experiments in order to test causal hypotheses and/or produce predictivemodels.One hundred sixty-six plots were placed in four different habitats along the Little Tennessee River where A. carolinensis occurs. Plots were surveyed for the presence/absence of this species in summer and winter seasons and habitat variables, both in and adjacent to the plots, were measured. Logistic regression modeling using the GAIM approach was conducted separately on the summer and winter data sets. For the summer data, the most frequent variables in the final set of GA models were(including the intercept): distance to potential overwintering rock, summercanopy categorization, distance to habitat edge, herb/shrub/vine cover,swimmer sunlight index, ambient temperature, and standardized distance along the habitat edge from the west boundary of habitat.For the winter data, the most frequent variables in the final set of models were (including the intercept): ambient temperature, presence of live overstory evergreen tree trunks, presence of overwintering rock,standardized distance along the habitat edge from the west boundary of habitat, distance to potential overwintering rock, and canopy cover categorization. In each data set, the variables which most frequently occurred in the final model set were also the ones which most frequently assessed statistically significant parameter estimates.The summer models suggest that further research on A. carolinensis might focus on a) sunlight and thermal factors and b) habitat features related to certain spatial scales beyond the skimmer home range scale.Future research might also examine responses of this species to winter habitat features such as a) shelter and potential basking sites, b) sunlight availability and temperature, and c) spatial features beyond the typical winter home range size. Methods using experimental control, or at least partial control, over field variables are needed to determine the specific responses of this species to key habitat features and the causal mechanisms underlying those responses. In addition, more studies are needed whichtake approaches based on biophysical and physiological ecology, especially if they can be linked to reproductive output, population ecology, and habitat use on local and regional scales

The 25th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting

Papers in the following categories are presented: recent developments in rubidium, cesium, and hydrogen-based frequency standards, and in cryogenic and trapped-ion technology; international and transnational applications of precise time and time interval (PTTI) technology with emphasis on satellite laser tracking networks, GLONASS timing, intercomparison of national time scales and international telecommunication; applications of PTTI technology to the telecommunications, power distribution, platform positioning, and geophysical survey industries; application of PTTI technology to evolving military communications and navigation systems; and dissemination of precise time and frequency by means of GPS, GLONASS, MILSTAR, LORAN, and synchronous communications satellites