44,047 research outputs found
Online Bin Covering with Exact Parameter Advice
We show an asymptotic 2/3-competitive strategy for the bin covering problem
using O(b+log n) bits of advice, where b is the number of bits used to encode a
rational value and n is the length of the input sequence.Comment: 10 pages, 2 figure, submitted to Informatic
The Advice Complexity of a Class of Hard Online Problems
The advice complexity of an online problem is a measure of how much knowledge
of the future an online algorithm needs in order to achieve a certain
competitive ratio. Using advice complexity, we define the first online
complexity class, AOC. The class includes independent set, vertex cover,
dominating set, and several others as complete problems. AOC-complete problems
are hard, since a single wrong answer by the online algorithm can have
devastating consequences. For each of these problems, we show that
bits of advice are
necessary and sufficient (up to an additive term of ) to achieve a
competitive ratio of .
The results are obtained by introducing a new string guessing problem related
to those of Emek et al. (TCS 2011) and B\"ockenhauer et al. (TCS 2014). It
turns out that this gives a powerful but easy-to-use method for providing both
upper and lower bounds on the advice complexity of an entire class of online
problems, the AOC-complete problems.
Previous results of Halld\'orsson et al. (TCS 2002) on online independent
set, in a related model, imply that the advice complexity of the problem is
. Our results improve on this by providing an exact formula for
the higher-order term. For online disjoint path allocation, B\"ockenhauer et
al. (ISAAC 2009) gave a lower bound of and an upper bound of
on the advice complexity. We improve on the upper bound by a
factor of . For the remaining problems, no bounds on their advice
complexity were previously known.Comment: Full paper to appear in Theory of Computing Systems. A preliminary
version appeared in STACS 201
Learning-Assisted Automated Reasoning with Flyspeck
The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
Application of machine learning to support self-management of asthma with mHealth
While there have been several efforts to use mHealth technologies to support asthma management, none so far offer personalised algorithms that can provide real-time feedback and tailored advice to patients based on their monitoring. This work employed a publicly available mHealth dataset, the Asthma Mobile Health Study (AMHS), and applied machine learning techniques to develop early warning algorithms to enhance asthma self-management. The AMHS consisted of longitudinal data from 5,875 patients, including 13,614 weekly surveys and 75,795 daily surveys. We applied several well-known supervised learning algorithms (classification) to differentiate stable and unstable periods and found that both logistic regression and naïve Bayes-based classifiers provided high accuracy (AUC > 0.87). We found features related to the use of quick-relief puffs, night symptoms, frequency of data entry, and day symptoms (in descending order of importance) as the most useful features to detect early evidence of loss of control. We found no additional value of using peak flow readings to improve population level early warning algorithms
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