287 research outputs found
Optimal Alphabetic Ternary Trees
We give a new algorithm to construct optimal alphabetic ternary trees, where
every internal node has at most three children. This algorithm generalizes the
classic Hu-Tucker algorithm, though the overall computational complexity has
yet to be determined
Sorting a Low-Entropy Sequence
We give the first sorting algorithm with bounds in terms of higher-order
entropies: let be a sequence of length containing distinct elements
and let (H_\ell (S)) be the th-order empirical entropy of , with
(n^{\ell + 1} \log n \in O (m)); our algorithm sorts using ((H_\ell (S) + O
(1)) m) comparisons
Codes : unequal probabilities, unequal letter costs
The construction of alphabetic prefix codes with unequal letter costs and unequal probabilities is considered. A variant of the noiseless coding theorem is proved giving closely matching lower and upper bounds for the cost of the optimal code. Furthermore, an algorithm is described which constructs a nearly optimal code in linear time
New Algorithms and Lower Bounds for Sequential-Access Data Compression
This thesis concerns sequential-access data compression, i.e., by algorithms
that read the input one or more times from beginning to end. In one chapter we
consider adaptive prefix coding, for which we must read the input character by
character, outputting each character's self-delimiting codeword before reading
the next one. We show how to encode and decode each character in constant
worst-case time while producing an encoding whose length is worst-case optimal.
In another chapter we consider one-pass compression with memory bounded in
terms of the alphabet size and context length, and prove a nearly tight
tradeoff between the amount of memory we can use and the quality of the
compression we can achieve. In a third chapter we consider compression in the
read/write streams model, which allows us passes and memory both
polylogarithmic in the size of the input. We first show how to achieve
universal compression using only one pass over one stream. We then show that
one stream is not sufficient for achieving good grammar-based compression.
Finally, we show that two streams are necessary and sufficient for achieving
entropy-only bounds.Comment: draft of PhD thesi
GPML: an XML-based standard for the interchange of genetic programming trees
We propose a Genetic Programming Markup Language (GPML), an XML based standard for the interchange of genetic programming trees, and outline the benefits such a format would bring in allowing the deployment of trained genetic
programming (GP) models in applications as well as the subsidiary benefit of allowing GP researchers to directly share trained trees. We present a formal definition of this standard and describe details of an implementation. In addition, we present a case study where GPML is used to implement a model predictive controller for the control of a building heating plant
Codes : unequal probabilities, unequal letter costs
The construction of alphabetic prefix codes with unequal letter costs and unequal probabilities is considered. A variant of the noiseless coding theorem is proved giving closely matching lower and upper bounds for the cost of the optimal code. Furthermore, an algorithm is described which constructs a nearly optimal code in linear time
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