@inproceedings{2891,
abstract = {Quantitative automata are nondeterministic finite automata with edge weights. They value a
run by some function from the sequence of visited weights to the reals, and value a word by its
minimal/maximal run. They generalize boolean automata, and have gained much attention in
recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and
limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential
of approximate determinization. We define approximate determinization with respect to
a distance function, and investigate this potential.
We show that sum automata cannot be determinized approximately with respect to any
distance function. However, restricting to nonnegative weights allows for approximate determinization
with respect to some distance functions.
Discounted-sum automata allow for approximate determinization, as the influence of a word’s
suffix is decaying. However, the naive approach, of unfolding the automaton computations up
to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an
alternative construction that is singly exponential in the discount factor, in the precision, and
in the number of states. We prove matching lower bounds, showing exponential dependency on
each of these three parameters.
Average and limit-average automata are shown to prohibit approximate determinization with
respect to any distance function, and this is the case even for two weights, 0 and 1.},
author = {Boker, Udi and Henzinger, Thomas A},
booktitle = {Leibniz International Proceedings in Informatics},
location = {Hyderabad, India},
pages = {362 -- 373},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Approximate determinization of quantitative automata}},
doi = {10.4230/LIPIcs.FSTTCS.2012.362},
volume = {18},
year = {2012},
}
@article{2902,
abstract = {We present an algorithm for simplifying linear cartographic objects and results obtained with a computer program implementing this algorithm. },
author = {Edelsbrunner, Herbert and Musin, Oleg and Ukhalov, Alexey and Yakimova, Olga and Alexeev, Vladislav and Bogaevskaya, Victoriya and Gorohov, Andrey and Preobrazhenskaya, Margarita},
journal = {Modeling and Analysis of Information Systems},
number = {6},
pages = {152 -- 160},
publisher = {Technische Universität Darmstadt},
title = {{Fractal and computational geometry for generalizing cartographic objects}},
volume = {19},
year = {2012},
}
@inproceedings{2903,
abstract = {In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images.},
author = {Edelsbrunner, Herbert and Symonova, Olga},
location = {New Brunswick, NJ, USA },
pages = {41 -- 48},
publisher = {IEEE},
title = {{The adaptive topology of a digital image}},
doi = {10.1109/ISVD.2012.11},
year = {2012},
}
@article{2904,
abstract = {Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences.},
author = {Pausinger, Florian},
issn = {2118-8572},
journal = {Journal de Theorie des Nombres des Bordeaux},
number = {3},
pages = {729 -- 749},
publisher = {Universite de Bordeaux},
title = {{Weak multipliers for generalized van der Corput sequences}},
doi = {10.5802/jtnb.819},
volume = {24},
year = {2012},
}
@article{2912,
author = {Edelsbrunner, Herbert and Strelkova, Nataliya},
journal = { Uspekhi Mat. Nauk},
number = {6},
pages = {203 -- 204},
publisher = {Moscow Mathematical Society },
title = {{Configuration space for shortest networks }},
doi = {10.4213/rm9503},
volume = {67},
year = {2012},
}