Improved Bounds for Open Online Dial-a-Ride on the Line

We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is the first bound that strictly separates online Dial-a-Ride on the line from online TSP on the line in terms of competitive analysis, and is the best currently known lower bound even for general metric spaces. On the other hand, we present an algorithm that improves the best known upper bound from 2.9377 to 2.6662. The analysis of our algorithm is tight

Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line

The online Dial-a-Ride problem is a fundamental online problem in a metric space, where transportation requests appear over time and may be served in any order by a single server with unit speed. Restricted to the real line, online Dial-a-Ride captures natural problems like controlling a personal elevator. Tight results in terms of competitive ratios are known for the general setting and for online TSP on the line (where source and target of each request coincide). In contrast, online Dial-a-Ride on the line has resisted tight analysis so far, even though it is a very natural online problem. We conduct a tight competitive analysis of the Smartstart algorithm that gave the best known results for the general, metric case. In particular, our analysis yields a new upper bound of 2.94 for open, non-preemptive online Dial-a-Ride on the line, which improves the previous bound of 3.41 [Krumke\u2700]. The best known lower bound remains 2.04 [SODA\u2717]. We also show that the known upper bound of 2 [STACS\u2700] regarding Smartstart\u27s competitive ratio for closed, non-preemptive online Dial-a-Ride is tight on the line

Improved Lower Bound for Competitive Graph Exploration

We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the agent has full knowledge of all edges incident to visited vertices, and, in particular, vertices have unique identifiers. Our bound improves a lower bound of 2.5 by Dobrev et al. [SIROCCO'12] and also holds for planar graphs, where it complements an upper bound of 16 by Kalyanasundaram and Pruhs[TCS'94]. The question whether a constant competitive ratio can be achieved in general remains open

Giordano Bruno: The Cosmic Perspective

Giordano Bruno (1548–1600) se v průběhu italské renesance etabloval jako nejvýznamnější filozof své doby. Odvážil se zpochybnit tehdy hluboce zakořeněný aristotelský světonázor. Bylo to díky síle jeho představivosti, která mu umožnila zajít ve svém hloubání až k úvahám o podstatě reality mimo naši Zemi. Jeho kosmická vize představovala náš vesmír jako nekonečný, obsahující nekonečné množství hvězd a planet, a dokonce uvažovala o možnosti existence inteligentních bytostí na jiných světech. V tomto byly Brunovy odvážné představy daleko před objevy Galilea, Koperníka, Keplera či Mikuláše Kusánského a dalších předních renesančních astronomů a filozofů. Právě Brunův úžasný vhled do metafyzické sféry položil základy dnešnímu vědeckému přístupu k pátrání po exoplanetách, neznámých formách života, sebeuvědomělých bytostech nebo i civilizacích, které mohou existovat někde v nedozírných hlubinách kosmického prostoru.During the Italian Renaissance, Giordano Bruno (1548-1600) emerged as the most significant philosopher of that time. He boldly challenged the deeply entrenched Aristotelian worldview by using his powerful imagination in order to speculate on the nature of reality beyond our earth. His cosmic vision claimed that this universe is eternal and contains an infinite number of stars and planets; it even held that intelligent beings exist on other worlds. As such, Bruno’s own daring ideas were far ahead of those discoveries that were made by Cusanus, Copernicus, Kepler, and Galileo (among other astronomers and philosophers of that age). In fact, it was his awesome metaphysical outlook that paved the way for our modern scientific search for those exoplanets, life forms, sentient creatures, and even civilizations that may exist elsewhere throughout the sidereal depths of outer space

Competitive analysis of the online dial-a-ride problem

Online optimization, in contrast to classical optimization, deals with optimization problems whose input data is not immediately available, but instead is revealed piece by piece. An online algorithm has to make irrevocable optimization decisions based on the arriving pieces of data to compute a solution of the online problem. The quality of an online algorithm is measured by the competitive ratio, which is the quotient of the solution computed by the online algorithm and the optimum offline solution, i.e., the solution computed by an optimum algorithm that has knowledge about all data from the start. In this thesis we examine the online optimization problem online Dial-a-Ride. This problem consists of a server starting at a distinct point of a metric space, called origin, and serving transportation requests that appear over time. The goal is to minimize the makespan, i.e., to complete serving all requests as fast as possible. We distinguish between a closed version, where the server is required to return to the origin, and an open version, where the server is allowed to stay at the destination of the last served request. In this thesis, we provide new lower bounds for the competitive ratio of online Dial-a-Ride on the real line for both the open and the closed version by expanding upon the approach of Bjelde et al.'s work. In the case of the open version, the improved lower bound separates online Dial-a-Ride from its special case online TSP, where starting position and destination of requests coincide. To produce improved upper bounds for the competitive ratio of online Dial-a-Ride, we generalize the design of the Ignore algorithm and the Smartstart algorithm into the class of schedule-based algorithms. We show lower bounds for the competitive ratios of algorithms of this class and then provide a thorough analysis of Ignore and Smartstart. Identifying and correcting a critical weakness of Smartstart gives us the improved Smarterstart algorithm. This schedule-based algorithm attains the best known upper bound for open online Dial-a-Ride on the real line as well as on arbitrary metric spaces. Finally, we provide an analysis of the Replan algorithm improving several known bounds for the algorithm's competitive ratio

The challenge of defining standards of prevention in HIV prevention trials.

As new HIV prevention tools are developed, researchers face a number of ethical and logistic questions about how and when to include novel HIV prevention strategies and tools in the standard prevention package of ongoing and future HIV prevention trials. Current Joint United Nations Programme on HIV/AIDS (UNAIDS)/World Health Organization (WHO) guidance recommends that participants in prevention trials receive 'access to all state of the art HIV risk reduction methods', and that decisions about adding new tools to the prevention package be made in consultation with 'all relevant stakeholders'. The guidance, however, leaves open questions of both process and implementation. In March 2009, the Global Campaign for Microbicides, UNAIDS and the Centers for Disease Control and Prevention convened a consultation to develop practical answers to these questions. Fifty-nine diverse participants, including researchers, ethicists, advocates and policymakers, worked to develop consensus criteria on when to include new HIV prevention tools in future trials. Participants developed a set of questions to guide decision-making, including: whether the method has been recommended by international bodies or adopted at a national level; the size of the effect and weight of the evidence; relevance to the trial population; whether the tool has been approved or introduced in the trial country; whether adding the tool might lead to trial futility; outstanding safety issues and status of the trial. Further work is needed to develop, implement and evaluate approaches to facilitate meaningful stakeholder participation in this deliberative process