2,487 research outputs found
Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem
In the minimum common string partition (MCSP) problem two related input
strings are given. "Related" refers to the property that both strings consist
of the same set of letters appearing the same number of times in each of the
two strings. The MCSP seeks a minimum cardinality partitioning of one string
into non-overlapping substrings that is also a valid partitioning for the
second string. This problem has applications in bioinformatics e.g. in
analyzing related DNA or protein sequences. For strings with lengths less than
about 1000 letters, a previously published integer linear programming (ILP)
formulation yields, when solved with a state-of-the-art solver such as CPLEX,
satisfactory results. In this work, we propose a new, alternative ILP model
that is compared to the former one. While a polyhedral study shows the linear
programming relaxations of the two models to be equally strong, a comprehensive
experimental comparison using real-world as well as artificially created
benchmark instances indicates substantial computational advantages of the new
formulation.Comment: arXiv admin note: text overlap with arXiv:1405.5646 This paper
version replaces the one submitted on January 10, 2015, due to detected error
in the calculation of the variables involved in the ILP model
Edit Distance: Sketching, Streaming and Document Exchange
We show that in the document exchange problem, where Alice holds and Bob holds , Alice can send Bob a message of
size bits such that Bob can recover using the
message and his input if the edit distance between and is no more
than , and output "error" otherwise. Both the encoding and decoding can be
done in time . This result significantly
improves the previous communication bounds under polynomial encoding/decoding
time. We also show that in the referee model, where Alice and Bob hold and
respectively, they can compute sketches of and of sizes
bits (the encoding), and send to the referee, who can
then compute the edit distance between and together with all the edit
operations if the edit distance is no more than , and output "error"
otherwise (the decoding). To the best of our knowledge, this is the first
result for sketching edit distance using bits.
Moreover, the encoding phase of our sketching algorithm can be performed by
scanning the input string in one pass. Thus our sketching algorithm also
implies the first streaming algorithm for computing edit distance and all the
edits exactly using bits of space.Comment: Full version of an article to be presented at the 57th Annual IEEE
Symposium on Foundations of Computer Science (FOCS 2016
Dissimilarity Clustering by Hierarchical Multi-Level Refinement
We introduce in this paper a new way of optimizing the natural extension of
the quantization error using in k-means clustering to dissimilarity data. The
proposed method is based on hierarchical clustering analysis combined with
multi-level heuristic refinement. The method is computationally efficient and
achieves better quantization errors than theComment: 20-th European Symposium on Artificial Neural Networks, Computational
Intelligence and Machine Learning (ESANN 2012), Bruges : Belgium (2012
Approximating reversal distance for strings with bounded number of duplicates
AbstractFor a string A=a1…an, a reversal ρ(i,j), 1⩽i⩽j⩽n, transforms the string A into a string A′=a1…ai-1ajaj-1…aiaj+1… an, that is, the reversal ρ(i,j) reverses the order of symbols in the substring ai…aj of A. In the case of signed strings, where each symbol is given a sign + or -, the reversal operation also flips the sign of each symbol in the reversed substring. Given two strings, A and B, signed or unsigned, sorting by reversals (SBR) is the problem of finding the minimum number of reversals that transform the string A into the string B.Traditionally, the problem was studied for permutations, that is, for strings in which every symbol appears exactly once. We consider a generalization of the problem, k-SBR, and allow each symbol to appear at most k times in each string, for some k⩾1. The main result of the paper is an O(k2)-approximation algorithm running in time O(n). For instances with 3<k⩽O(lognlog*n), this is the best known approximation algorithm for k-SBRand, moreover, it is faster than the previous best approximation algorithm
Fast Quasi-Threshold Editing
We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the
quasi-threshold (also called trivially perfect) graph editing problem with edge
insertion and deletion. Given a graph it computes a quasi-threshold graph which
is close in terms of edit count. This edit problem is NP-hard. We present an
extensive experimental study, in which we show that QTM is the first algorithm
that is able to scale to large real-world graphs in practice. As a side result
we further present a simple linear-time algorithm for the quasi-threshold
recognition problem.Comment: 26 pages, 4 figures, submitted to ESA 201
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