11,843 research outputs found
Faster Deterministic Fully-Dynamic Graph Connectivity
We give new deterministic bounds for fully-dynamic graph connectivity. Our
data structure supports updates (edge insertions/deletions) in
amortized time and connectivity queries in worst-case time, where is the number of vertices of the
graph. This improves the deterministic data structures of Holm, de Lichtenberg,
and Thorup (STOC 1998, J.ACM 2001) and Thorup (STOC 2000) which both have
amortized update time and worst-case query
time. Our model of computation is the same as that of Thorup, i.e., a pointer
machine with standard instructions.Comment: To appear at SODA 2013. 19 pages, 1 figur
Fully Dynamic Connectivity in Amortized Expected Time
Dynamic connectivity is one of the most fundamental problems in dynamic graph
algorithms. We present a randomized Las Vegas dynamic connectivity data
structure with amortized expected update time and
worst case query time, which comes very close to the
cell probe lower bounds of Patrascu and Demaine (2006) and Patrascu and Thorup
(2011)
Energy of taut strings accompanying Wiener process
Let be a Wiener process. The function minmizing energy
among all functions satisfying on an interval is called taut string. This is a classical
object well known in Variational Calculus, Mathematical Statistics, etc. We
show that the energy of this taut string on large intervals is equivalent to
where is some finite positive constant. While the precise
value of remains unknown, we give various theoretical bounds for it as well
as rather precise results of computer simulation.
While the taut string clearly depends on entire trajectory of , we also
consider an adaptive version of the problem by giving a construction (Markovian
pursuit) of a random function based only on the past values of and having
minimal asymptotic energy. The solution, an optimal pursuit strategy, quite
surprisingly turns out to be related with a classical minimization problem for
Fisher information on the bounded interval
Weaving Rules into [email protected] for Embedded Smart Systems
Smart systems are characterised by their ability to analyse measured data in
live and to react to changes according to expert rules. Therefore, such systems
exploit appropriate data models together with actions, triggered by
domain-related conditions. The challenge at hand is that smart systems usually
need to process thousands of updates to detect which rules need to be
triggered, often even on restricted hardware like a Raspberry Pi. Despite
various approaches have been investigated to efficiently check conditions on
data models, they either assume to fit into main memory or rely on high latency
persistence storage systems that severely damage the reactivity of smart
systems. To tackle this challenge, we propose a novel composition process,
which weaves executable rules into a data model with lazy loading abilities. We
quantitatively show, on a smart building case study, that our approach can
handle, at low latency, big sets of rules on top of large-scale data models on
restricted hardware.Comment: pre-print version, published in the proceedings of MOMO-17 Worksho
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