2,882 research outputs found
A Central Limit Theorem for the Length of the Longest Common Subsequences in Random Words
Let and be two independent sequences of
independent identically distributed random variables taking their values in a
common finite alphabet and having the same law. Let be the length of the
longest common subsequences of the two random words and
. Under a lower bound assumption on the order of its variance,
is shown to satisfy a central limit theorem. This is in contrast to the
limiting distribution of the length of the longest common subsequences in two
independent uniform random permutations of , which is shown to
be the Tracy-Widom distribution.Comment: Some corrections, typos corrected and improvement
On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences
It is well known that, when normalized by n, the expected length of a longest
common subsequence of d sequences of length n over an alphabet of size sigma
converges to a constant gamma_{sigma,d}. We disprove a speculation by Steele
regarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order to
do that we also obtain new lower bounds for gamma_{sigma,d}, when both sigma
and d are small integers.Comment: 13 pages. To appear in Combinatorics, Probability and Computin
On the limiting law of the length of the longest common and increasing subsequences in random words
Let and be two sequences of independent
and identically distributed (iid) random variables taking their values,
uniformly, in a common totally ordered finite alphabet. Let LCI be the
length of the longest common and (weakly) increasing subsequence of and . As grows without bound, and when properly
centered and normalized, LCI is shown to converge, in distribution, towards
a Brownian functional that we identify.Comment: Some corrections from the published version are provided, some typos
are also correcte
Expected length of the longest common subsequence for large alphabets
We consider the length L of the longest common subsequence of two randomly
uniformly and independently chosen n character words over a k-ary alphabet.
Subadditivity arguments yield that the expected value of L, when normalized by
n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville
from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe
Universality of the Distribution Functions of Random Matrix Theory. II
This paper is a brief review of recent developments in random matrix theory.
Two aspects are emphasized: the underlying role of integrable systems and the
occurrence of the distribution functions of random matrix theory in diverse
areas of mathematics and physics.Comment: 17 pages, 3 figure
Bounds on the Number of Longest Common Subsequences
This paper performs the analysis necessary to bound the running time of
known, efficient algorithms for generating all longest common subsequences.
That is, we bound the running time as a function of input size for algorithms
with time essentially proportional to the output size. This paper considers
both the case of computing all distinct LCSs and the case of computing all LCS
embeddings. Also included is an analysis of how much better the efficient
algorithms are than the standard method of generating LCS embeddings. A full
analysis is carried out with running times measured as a function of the total
number of input characters, and much of the analysis is also provided for cases
in which the two input sequences are of the same specified length or of two
independently specified lengths.Comment: 13 pages. Corrected typos, corrected operation of hyperlinks,
improved presentatio
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