Since its introduction in 1985, competitive analysis is a widely used tool for the performance measurement of online algorithms. Despite its simplicity and popularity, competitive analysis has its own set of drawbacks which lead to the development of other performance measures. However, these measures were seldom applied to problems in other domains. Recently Boyar et al. (Theor. Comput. Sci. 532 (2014) 2–13) studied the online search problem using various performance analysis measures for non-preemptive algorithms. We extend the work by considering preemptive threat-based algorithms and evaluate it using competitive analysis, bijective analysis, average case and relative interval analysis. For competitive analysis, and average case analysis, our findings are in contrast with that of Boyar et al., whereas for bijective and relative interval analysis our findings complement that of Boyar et al.

In this work we investigate theportfolio selection problem(P1) andbi-directional trading(P2) when prices are interrelated. Zhanget al.(J. Comb. Optim.23(2012) 159–166) provided the algorithm UND which solves one variant of P2. We are interested in solutions which are optimal from a worst-case perspective. For P1, we prove the worst-case input sequence and derive the algorithmoptimal portfolio for interrelated prices(OPIP). We then prove the competitive ratio and optimality. We use the idea of OPIP to solve P2 and derive the algorithm calledoptimal conversion for interrelated prices(OCIP). Using OCIP, we also design optimal online algorithms forbi-directional search(P3) calledbi-directional UND(BUND) andoptimal online search for unknown relative price bounds(RUN). We run numerical experiments and conclude that OPIP and OCIP perform well compared to other algorithms even if prices do not behave adverse.

We consider the online problems of time series search and one-way trading with interrelated prices. We derive two algorithms PUND and PDIV which extend the solutions found in literature with profit functions, derive the competitive ratio and prove optimality. For the new as well as for the established online algorithms, we give a numerical example. For the time series search problem with interrelated prices, we present another algorithm UND∗. This algorithm has constant time complexity and an explicit formula for the competitive ratio and selected period to sell. The current solution in literature has linear time complexity and no such explicit formulas.

We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.

In an online conversion problem a player is converting one asset into another, e.g. dollars to yen, based on a finite sequence of unknown future conversion rates. When a new rate is announced the player must decide how many dollars (yen) to convert to yen (dollars) according to this rate. Conversion is over when the last rate has appeared. The objective is to maximize terminal wealth after conversion. In uni-directional conversion dollars are converted to yen and in bi-directional conversion not only dollars to yen but also yen to dollars may be converted. If all current wealth has to be converted at one rate we call the problem non-preemptive; if parts of the current wealth can be converted at one rate we call it preemptive. We assume that lower and upper bounds on conversion rates are given. Uni-directional preemptive and non-preemptive and bi-directional preemptive conversion is investigated in El Yaniv et al. (Proceeding 33rd annual symposium on foundations of computer science, pp 327–333, 1992, Algorithmica 30:101–139, 2001). Their results for bi-directional preemptive conversion are improved by Dannoura and Sakurai (Inf Process Lett 66:27–33, 1998). The suggested improvement is conjectured not to be optimal for bi-directional preemptive conversion. There are no results for optimal bi-directional non-preemptive conversion. We investigate the problem of bi-directional non-preemptive online conversion. We present lower bounds, upper bounds and an optimal algorithm to solve the problem. Moreover, we prove that the algorithm of Dannoura and Sakurai 1998 is not optimal for bi-directional preemptive conversion.

We consider bi-directional non-preemptive conversion with interrelated conversion rate bounds. We solve this conversion problem with two on-line algorithms BUND and RUN and give their competitive ratio. We further observe optimality of both on-line algorithms. We also use empirical data of the Johannesburg Stock Exchange to get further insights into RUN and BUND.

BACKGROUND:Biobanks increasingly presume long-term storage of biomaterials and data that shall be used for future research projects which are today unspecified. Appropriate consent documents for sample donors must therefore explain the breadth of consent and other elements of the biobank governance framework. Recent reviews demonstrated high variability in what issues these documents mention or not and how the issues are explained. This might undermine the protection of sample donors, complicate networked biobank research, create research waste and impact on public trust. METHODS:A systematic analysis of international research guidelines and existing broad consent templates was performed. Based on this information an interdisciplinary expert group from the AKMEK (Permanent Working Party of German RECs) developed a draft template and organized a comprehensive stakeholder consultation. After revision the final template was consented by all 53 German RECs. RESULTS:This paper briefly explores the spectrum of potentially relevant issues for broad consent forms. It then elaborates the template and how it was designed to be applicable in different types of biobanks. DISCUSSION:To further improve the validity and applicability of broad consent forms in biobank and other big data research, practice evaluations are needed. We hope that in this regard the presented template supports the development of new consent forms as well as the evaluation and revision of existing ones.