232,077 research outputs found
Time lower bounds for nonadaptive turnstile streaming algorithms
We say a turnstile streaming algorithm is "non-adaptive" if, during updates,
the memory cells written and read depend only on the index being updated and
random coins tossed at the beginning of the stream (and not on the memory
contents of the algorithm). Memory cells read during queries may be decided
upon adaptively. All known turnstile streaming algorithms in the literature are
non-adaptive.
We prove the first non-trivial update time lower bounds for both randomized
and deterministic turnstile streaming algorithms, which hold when the
algorithms are non-adaptive. While there has been abundant success in proving
space lower bounds, there have been no non-trivial update time lower bounds in
the turnstile model. Our lower bounds hold against classically studied problems
such as heavy hitters, point query, entropy estimation, and moment estimation.
In some cases of deterministic algorithms, our lower bounds nearly match known
upper bounds
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Testing in the distributed test architecture: An extended abstract
Some systems interact with their environment at a number of physically distributed interfaces/ports and when testing such a system it is normal to place a local tester at each port. If the local testers cannot interact with one another and there is no global clock then we are testing in the distributed test architecture and this can introduce additional controllability and observability problems. While there has been interest in test generation algorithms that overcome controllability and observability problems, such algorithms lack generality since controllability and observability problems cannot always be overcome. In addition, traditionally only deterministic systems and models have been considered despite distributed systems often being non-deterministic. This paper describes recent work that characterized the power of testing in the distributed test architecture in the context of testing from a deterministic finite state machine and also work that investigated testing from a non-deterministic finite state machine and testing from an input output transition system. This work has the potential to lead to more general test generation algorithms for the distributed test architecture
Deterministic Sampling and Range Counting in Geometric Data Streams
We present memory-efficient deterministic algorithms for constructing
epsilon-nets and epsilon-approximations of streams of geometric data. Unlike
probabilistic approaches, these deterministic samples provide guaranteed bounds
on their approximation factors. We show how our deterministic samples can be
used to answer approximate online iceberg geometric queries on data streams. We
use these techniques to approximate several robust statistics of geometric data
streams, including Tukey depth, simplicial depth, regression depth, the
Thiel-Sen estimator, and the least median of squares. Our algorithms use only a
polylogarithmic amount of memory, provided the desired approximation factors
are inverse-polylogarithmic. We also include a lower bound for non-iceberg
geometric queries.Comment: 12 pages, 1 figur
Bounded Determinization of Timed Automata with Silent Transitions
Deterministic timed automata are strictly less expressive than their
non-deterministic counterparts, which are again less expressive than those with
silent transitions. As a consequence, timed automata are in general
non-determinizable. This is unfortunate since deterministic automata play a
major role in model-based testing, observability and implementability. However,
by bounding the length of the traces in the automaton, effective
determinization becomes possible. We propose a novel procedure for bounded
determinization of timed automata. The procedure unfolds the automata to
bounded trees, removes all silent transitions and determinizes via disjunction
of guards. The proposed algorithms are optimized to the bounded setting and
thus are more efficient and can handle a larger class of timed automata than
the general algorithms. The approach is implemented in a prototype tool and
evaluated on several examples. To our best knowledge, this is the first
implementation of this type of procedure for timed automata.Comment: 25 page
Routing on the Visibility Graph
We consider the problem of routing on a network in the presence of line
segment constraints (i.e., obstacles that edges in our network are not allowed
to cross). Let be a set of points in the plane and let be a set of
non-crossing line segments whose endpoints are in . We present two
deterministic 1-local -memory routing algorithms that are guaranteed to
find a path of at most linear size between any pair of vertices of the
\emph{visibility graph} of with respect to a set of constraints (i.e.,
the algorithms never look beyond the direct neighbours of the current location
and store only a constant amount of additional information). Contrary to {\em
all} existing deterministic local routing algorithms, our routing algorithms do
not route on a plane subgraph of the visibility graph. Additionally, we provide
lower bounds on the routing ratio of any deterministic local routing algorithm
on the visibility graph.Comment: An extended abstract of this paper appeared in the proceedings of the
28th International Symposium on Algorithms and Computation (ISAAC 2017).
Final version appeared in the Journal of Computational Geometr
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