1,614 research outputs found
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational
geometry is presented.Comment: 7 pages; 72 reference
Graph- versus Vector-Based Analysis of a Consensus Protocol
The Paxos distributed consensus algorithm is a challenging case-study for
standard, vector-based model checking techniques. Due to asynchronous
communication, exhaustive analysis may generate very large state spaces already
for small model instances. In this paper, we show the advantages of graph
transformation as an alternative modelling technique. We model Paxos in a rich
declarative transformation language, featuring (among other things) nested
quantifiers, and we validate our model using the GROOVE model checker, a
graph-based tool that exploits isomorphism as a natural way to prune the state
space via symmetry reductions. We compare the results with those obtained by
the standard model checker Spin on the basis of a vector-based encoding of the
algorithm.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767
A Call to Arms: Revisiting Database Design
Good database design is crucial to obtain a sound, consistent database, and -
in turn - good database design methodologies are the best way to achieve the
right design. These methodologies are taught to most Computer Science
undergraduates, as part of any Introduction to Database class. They can be
considered part of the "canon", and indeed, the overall approach to database
design has been unchanged for years. Moreover, none of the major database
research assessments identify database design as a strategic research
direction.
Should we conclude that database design is a solved problem?
Our thesis is that database design remains a critical unsolved problem.
Hence, it should be the subject of more research. Our starting point is the
observation that traditional database design is not used in practice - and if
it were used it would result in designs that are not well adapted to current
environments. In short, database design has failed to keep up with the times.
In this paper, we put forth arguments to support our viewpoint, analyze the
root causes of this situation and suggest some avenues of research.Comment: Removed spurious column break. Nothing else was change
New Developments in Quantum Algorithms
In this survey, we describe two recent developments in quantum algorithms.
The first new development is a quantum algorithm for evaluating a Boolean
formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This
provides quantum speedups for any problem that can be expressed via Boolean
formulas. This result can be also extended to span problems, a generalization
of Boolean formulas. This provides an optimal quantum algorithm for any Boolean
function in the black-box query model.
The second new development is a quantum algorithm for solving systems of
linear equations. In contrast with traditional algorithms that run in time
O(N^{2.37...}) where N is the size of the system, the quantum algorithm runs in
time O(\log^c N). It outputs a quantum state describing the solution of the
system.Comment: 11 pages, 1 figure, to appear as an invited survey talk at MFCS'201
Quantum strategies
We consider game theory from the perspective of quantum algorithms.
Strategies in classical game theory are either pure (deterministic) or mixed
(probabilistic). We introduce these basic ideas in the context of a simple
example, closely related to the traditional Matching Pennies game. While not
every two-person zero-sum finite game has an equilibrium in the set of pure
strategies, von Neumann showed that there is always an equilibrium at which
each player follows a mixed strategy. A mixed strategy deviating from the
equilibrium strategy cannot increase a player's expected payoff. We show,
however, that in our example a player who implements a quantum strategy can
increase his expected payoff, and explain the relation to efficient quantum
algorithms. We prove that in general a quantum strategy is always at least as
good as a classical one, and furthermore that when both players use quantum
strategies there need not be any equilibrium, but if both are allowed mixed
quantum strategies there must be.Comment: 8 pages, plain TeX, 1 figur
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