1,407 research outputs found
Random Access to Grammar Compressed Strings
Grammar based compression, where one replaces a long string by a small
context-free grammar that generates the string, is a simple and powerful
paradigm that captures many popular compression schemes. In this paper, we
present a novel grammar representation that allows efficient random access to
any character or substring without decompressing the string.
Let be a string of length compressed into a context-free grammar
of size . We present two representations of
achieving random access time, and either
construction time and space on the pointer machine model, or
construction time and space on the RAM. Here, is the inverse of
the row of Ackermann's function. Our representations also efficiently
support decompression of any substring in : we can decompress any substring
of length in the same complexity as a single random access query and
additional time. Combining these results with fast algorithms for
uncompressed approximate string matching leads to several efficient algorithms
for approximate string matching on grammar-compressed strings without
decompression. For instance, we can find all approximate occurrences of a
pattern with at most errors in time , where is the number of occurrences of in . Finally, we
generalize our results to navigation and other operations on grammar-compressed
ordered trees.
All of the above bounds significantly improve the currently best known
results. To achieve these bounds, we introduce several new techniques and data
structures of independent interest, including a predecessor data structure, two
"biased" weighted ancestor data structures, and a compact representation of
heavy paths in grammars.Comment: Preliminary version in SODA 201
Impact of loss on the wave dynamics in photonic waveguide lattices
We analyze the impact of loss in lattices of coupled optical waveguides and
find that in such case, the hopping between adjacent waveguides is necessarily
complex. This results not only in a transition of the light spreading from
ballistic to diffusive, but also in a new kind of diffraction that is caused by
loss dispersion. We prove our theoretical results with experimental
observations.Comment: Accepted for publication in PRL, 5+8 pages (Paper + Supplemental
material), 4 figure
The effect of thermal annealing on the properties of Al-AlOx-Al single electron tunneling transistors
The effect of thermal annealing on the properties of Al-AlOx-Al single
electron tunneling transistors is reported. After treatment of the devices by
annealing processes in forming gas atmosphere at different temperatures and for
different times, distinct and reproducible changes of their resistance and
capacitance values were found. According to the temperature regime, we observed
different behaviors as regards the resistance changes, namely the tendency to
decrease the resistance by annealing at T = 200 degree C, but to increase the
resistance by annealing at T = 400 degree C. We attribute this behavior to
changes in the aluminum oxide barriers of the tunnel junctions. The good
reproducibility of these effects with respect to the changes observed allows
the proper annealing treatment to be used for post-process tuning of tunnel
junction parameters. Also, the influence of the annealing treatment on the
noise properties of the transistors at low frequency was investigated. In no
case did the noise figures in the 1/f-regime show significant changes.Comment: 6 pages, 7 eps-figure
An O(n^3)-Time Algorithm for Tree Edit Distance
The {\em edit distance} between two ordered trees with vertex labels is the
minimum cost of transforming one tree into the other by a sequence of
elementary operations consisting of deleting and relabeling existing nodes, as
well as inserting new nodes. In this paper, we present a worst-case
-time algorithm for this problem, improving the previous best
-time algorithm~\cite{Klein}. Our result requires a novel
adaptive strategy for deciding how a dynamic program divides into subproblems
(which is interesting in its own right), together with a deeper understanding
of the previous algorithms for the problem. We also prove the optimality of our
algorithm among the family of \emph{decomposition strategy} algorithms--which
also includes the previous fastest algorithms--by tightening the known lower
bound of ~\cite{Touzet} to , matching our
algorithm's running time. Furthermore, we obtain matching upper and lower
bounds of when the two trees have
different sizes and~, where .Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on
Top Tree Compression of Tries
We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to preprocess a set of strings of total length n over an alphabet of size sigma into a compressed data structure of worst-case optimal size O(n/log_sigma n) that given a pattern string P of length m determines if P is a prefix of one of the strings in time O(min(m log sigma,m + log n)). We show that this query time is in fact optimal regardless of the size of the data structure.
Existing solutions either use Omega(n) space or rely on word RAM techniques, such as tabulation, hashing, address arithmetic, or word-level parallelism, and hence do not work on a pointer machine. Our result is the first solution on a pointer machine that achieves worst-case o(n) space. Along the way, we develop several interesting data structures that work on a pointer machine and are of independent interest. These include an optimal data structures for random access to a grammar-compressed string and an optimal data structure for a variant of the level ancestor problem
The Nearest Colored Node in a Tree
We start a systematic study of data structures for the nearest colored node problem on trees. Given a tree with colored nodes and weighted edges, we want to answer queries (v,c) asking for the nearest node to node v that has color c. This is a natural generalization of the well-known nearest marked ancestor problem. We give an O(n)-space O(log log n)-query solution and show that this is optimal. We also consider the dynamic case where updates can change a node\u27s color and show that in O(n) space we can support both updates and queries in O(log n) time. We complement this by showing that O(polylog n) update time implies Omega(log n log log n) query time. Finally, we consider the case where updates can change the edges of the tree (link-cut operations). There is a known (top-tree based) solution that requires update time that is roughly linear in the number of colors. We show that this solution is probably optimal by showing that a strictly sublinear update time implies a strictly subcubic time algorithm for the classical all pairs shortest paths problem on a general graph. We also consider versions where the tree is rooted, and the query asks for the nearest ancestor/descendant of node v that has color c, and present efficient data structures for both variants in the static and the dynamic setting
A stringent yeast two-hybrid matrix screening approach for protein-protein interaction discovery
The yeast two-hybrid (Y2H) system is currently one of the most important techniques for protein-protein interaction (PPI) discovery. Here, we describe a stringent three-step Y2H matrix interaction approach that is suitable for systematic PPI screening on a proteome scale. We start with the identification and elimination of autoactivating strains that would lead to false-positive signals and prevent the identification of interactions. Nonautoactivating strains are used for the primary PPI screen that is carried out in quadruplicate with arrayed preys. Interacting pairs of baits and preys are identified in a pairwise retest step. Only PPI pairs that pass the retest step are regarded as potentially biologically relevant interactions and are considered for further analysis
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