56 research outputs found
10231 Abstracts Collection -- Structure Discovery in Biology: Motifs, Networks & Phylogenies
From 06.06. to 11.06.2010, the Dagstuhl Seminar 10231 ``Structure Discovery in Biology: Motifs, Networks & Phylogenies \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
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
On the Comparison Complexity of the String Prefix-Matching Problem
In this paper we study the exact comparison complexity of the stringprefix-matching problem in the deterministic sequential comparison modelwith equality tests. We derive almost tight lower and upper bounds onthe number of symbol comparisons required in the worst case by on-lineprefix-matching algorithms for any fixed pattern and variable text. Unlikeprevious results on the comparison complexity of string-matching andprefix-matching algorithms, our bounds are almost tight for any particular pattern.We also consider the special case where the pattern and the text are thesame string. This problem, which we call the string self-prefix problem, issimilar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matchingalgorithm that is used in several comparison efficient string-matchingand prefix-matching algorithms, including in our new algorithm.We obtain roughly tight lower and upper bounds on the number of symbolcomparisons required in the worst case by on-line self-prefix algorithms.Our algorithms can be implemented in linear time and space in thestandard uniform-cost random-access-machine model
Multivariate Fine-Grained Complexity of Longest Common Subsequence
We revisit the classic combinatorial pattern matching problem of finding a
longest common subsequence (LCS). For strings and of length , a
textbook algorithm solves LCS in time , but although much effort has
been spent, no -time algorithm is known. Recent work
indeed shows that such an algorithm would refute the Strong Exponential Time
Hypothesis (SETH) [Abboud, Backurs, Vassilevska Williams + Bringmann,
K\"unnemann FOCS'15].
Despite the quadratic-time barrier, for over 40 years an enduring scientific
interest continued to produce fast algorithms for LCS and its variations.
Particular attention was put into identifying and exploiting input parameters
that yield strongly subquadratic time algorithms for special cases of interest,
e.g., differential file comparison. This line of research was successfully
pursued until 1990, at which time significant improvements came to a halt. In
this paper, using the lens of fine-grained complexity, our goal is to (1)
justify the lack of further improvements and (2) determine whether some special
cases of LCS admit faster algorithms than currently known.
To this end, we provide a systematic study of the multivariate complexity of
LCS, taking into account all parameters previously discussed in the literature:
the input size , the length of the shorter string
, the length of an LCS of and , the numbers of
deletions and , the alphabet size, as well as
the numbers of matching pairs and dominant pairs . For any class of
instances defined by fixing each parameter individually to a polynomial in
terms of the input size, we prove a SETH-based lower bound matching one of
three known algorithms. Specifically, we determine the optimal running time for
LCS under SETH as .
[...]Comment: Presented at SODA'18. Full Version. 66 page
Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS
We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size |Sigma|. For the problem of deciding whether the LCS of strings x,y has length at least L, we obtain a sketch size and streaming space usage of O(L^{|Sigma| - 1} log L). We also prove matching unconditional lower bounds.
As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an O(min{nm, n + m^{|Sigma|}})-time algorithm for this problem, on strings x,y of length n,m, with n >= m. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis
- …