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The correctness proof of Ben-Or’s randomized consensus algorithm
In a ground-breaking paper that appeared in 1983, Ben-Or presented the first randomized algorithm to solve consensus in an asynchronous message-passing system where processes can fail by crashing. Although more efficient randomized algorithms were subsequently proposed, Ben-Or’s algorithm is still the simplest and most elegant one. For this reason, it is often taught in distributed computing courses and it appears in several textbooks. Even though Ben-Or’s algorithm is widely known and it is very simple, surprisingly a proof of correctness of the algorithm has not yet appeared: previously published proofs make some simplifying assumptions—specifically, they either assume that
f
<
n
/3 (
n
is the total number of processes and
f
is maximum number of processes that may crash) or that the adversary is weak, that is, it cannot see the process states or the content of the messages. In this paper, we present a correctness proof for Ben-Or’s randomized consensus algorithm for the case that
f
<
n
/2 process crashes and the adversary is strong (i.e., it can see the process states and message contents, and schedule the process steps and message receipts accordingly). To the best of our knowledge, this is the first full proof of this classical algorithm. We also demonstrate a counterintuitive problem that may occur if one uses the well-known abstraction of a “global coin” to modularize and speed up randomized consensus algorithms, such as Ben-Or’s algorithm. Specifically, we show that contrary to common belief, the use of a global coin can sometimes be deleterious rather than beneficial: instead of speeding up Ben-Or’s algorithm, the use of a global coin in this algorithm may actually prevent termination.
Journal Article
Results of a Research Evaluating Quality of Computer Science Education
The paper presents the results of an international research on a comparative assessment
of the current status of computer science education at the secondary level (ISCED 3A) in Slovakia,
the Czech Republic, and Belgium. Evaluation was carried out based on 14 specific factors
gauging the students’ point of view. The authors present qualitative findings from the following
nine analyzed factors: the popularity of computer science/informatics as a subject, the potential of
using knowledge gained by studying informatics at school in everyday life, the attractiveness and
demands of the curriculum content, the clarity and attractiveness of teacher presentation of the subject
matter to students, the engagement of tasks solved while studying informatics, the degree of
comprehensibility of informatics textbooks, and the usability of knowledge acquired in school for
solving practical problems. Based on the results, the authors identify the strengths and weaknesses
of computer science education in the observed countries.
Journal Article
The Recurrence Relations in Teaching Students of Informatics
The topic “Recurrence relations” and its place in teaching students of Informatics is discussed
in this paper. We represent many arguments about the importance, the necessity and the
benefit of studying this subject by Informatics students. They are based on investigation of some
fundamental books and textbooks on Discrete Mathematics, Algorithms and Data Structures, Combinatorics,
etc. Somemethodological aspects of training to solve problems with applying recurrence
relations are also given. We hope that the considered topics concern also the school teachers in
Mathematics and Informatics and the paper will be useful to them.
Journal Article
Confronting database complexities
Database technology is exploding, as the hierarchical and relational models give way to object-oriented, distributed heterogeneous, and other kinds of specialized models. Designers, programmers, and users need new tools.< >
Journal Article
New Factorizable Discretizations for the Euler Equations
A multigrid method is defined as having textbook multigrid efficiency (TME) if solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. A way to achieve TME for the Euler and Navier--Stokes equations is to apply the distributed relaxation method, thereby separating the elliptic and hyperbolic partitions of the equations. Design of a distributed relaxation scheme can be significantly simplified if the principal linearization of the target discretization possesses two properties: (1) factorizability and (2) consistent approximations for the separate factors. The first property implies that the discrete system determinant can be represented as a product of discrete factors, each of them approximating a corresponding factor of the determinant of the differential equations. The second property requires that the discrete factors reflect the physical anisotropies, be stable, and be easily solvable. This paper presents an approach to the derivation of discretization schemes for which TME can be achieved by multigrid solvers with distributed relaxation. In particular, discrete schemes for the nonconservative Euler equations possessing properties (1) and (2) have been derived and analyzed. The accuracy of these scheme has been tested for subsonic flow regimes and compared with accuracy of standard schemes. TME has been demonstrated in solving fully subsonic quasi--one-dimensional flow in a convergent/divergent channel.
Journal Article