139 research outputs found
Weighted Shortest Common Supersequence problem revisited
A weighted string, also known as a position weight matrix, is a sequence of probability distributions over some alphabet. We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is, the SCS problem on weighted strings. In the WSCS problem, we are given two weighted strings (Formula presented) and (Formula presented) and a threshold (Formula presented) on probability, and we are asked to compute the shortest (standard) string S such that both (Formula presented) and (Formula presented) match subsequences of S (not necessarily the same
A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics
From the output produced by a memoryless deletion channel from a uniformly
random input of known length , one obtains a posterior distribution on the
channel input. The difference between the Shannon entropy of this distribution
and that of the uniform prior measures the amount of information about the
channel input which is conveyed by the output of length , and it is natural
to ask for which outputs this is extremized. This question was posed in a
previous work, where it was conjectured on the basis of experimental data that
the entropy of the posterior is minimized and maximized by the constant strings
and and the alternating strings
and respectively. In the present
work we confirm the minimization conjecture in the asymptotic limit using
results from hidden word statistics. We show how the analytic-combinatorial
methods of Flajolet, Szpankowski and Vall\'ee for dealing with the hidden
pattern matching problem can be applied to resolve the case of fixed output
length and , by obtaining estimates for the entropy in
terms of the moments of the posterior distribution and establishing its
minimization via a measure of autocorrelation.Comment: 11 pages, 2 figure
The Loading Time Scheduling Problem
In this paper we study precedence constrained scheduling problems, where
the tasks can only be executed on a specified subset of the machines.
Each machine has a loading time that is incurred only for the first task
that is scheduled on the machine in a particular run. This basic
scheduling problem arises in the context of machining on numerically
controlled machines, query optimization in databases, and in other
artificial intelligence applications. We give the first non-trivial
approximation algorithm for this problem. We also prove non-trivial
lower bounds on best possible approximation ratios for these problems.
These improve on the non-approximability results that are implied by the
non-approximability results for the shortests common supersequence problem.
We use the same algorithmic technique to obtain approximation algorithms
for a problem arising in the context of code generation for parallel
machines, and for the weighted shortest common supersequence problem
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