93,075 research outputs found
Edit Distance with Block Operations
We consider the problem of edit distance in which block operations are allowed, i.e. we ask for the minimal number of (block) operations that are needed to transform a string s to t. We give O(log n) approximation algorithms, where n is the total length of the input strings, for the variants of the problem which allow the following sets of operations: block move; block move and block delete; block move and block copy; block move, block copy, and block uncopy. The results still hold if we additionally allow any of the following operations: character insert, character delete, block reversal, or block involution (involution is a generalisation of the reversal). Previously, algorithms only for the first and last variant were known, and they had approximation ratios O(log n log^*n) and O(log n (log^*n)^2), respectively. The edit distance with block moves is equivalent, up to a constant factor, to the common string partition problem, in which we are given two strings s, t and the goal is to partition s into minimal number of parts such that they can be permuted in order to obtain t. Thus we also obtain an O(log n) approximation for this problem (compared to the previous O(log n log^* n)).
The results use a simplification of the previously used technique of locally consistent parsing, which groups short substrings of a string into phrases so that similar substrings are guaranteed to be grouped in a similar way. Instead of a sophisticated parsing technique relying on a deterministic coin tossing, we use a simple one based on a partition of the alphabet into two subalphabets. In particular, this lowers the running time from O(n log^* n) to O(n). The new algorithms (for block copy or block delete) use a similar algorithm, but the analysis is based on a specially tuned combinatorial function on sets of numbers
An efficient algorithm for sequence comparison with block reversals
AbstractGiven two sequences X and Y that are strings over some alphabet set, we consider the distance d(X,Y) between them defined to be minimum number of character replacements and block (substring) reversals needed to transform X to Y (or vice versa). The operations are required to be disjoint. This is the βsimplestβ sequence comparison problem we know of that allows natural block edit operations. Block reversals arise naturally in genomic sequence comparison; they are also of interest in matching music data. We present an algorithm for exactly computing the distance d(X,Y); it takes time O(|X|log2|X|), and hence, is near-linear. Trivial approach takes quadratic time
Efficient Algorithms for Fast Integration on Large Data Sets from Multiple Sources
Background
Recent large scale deployments of health information technology have created opportunities for the integration of patient medical records with disparate public health, human service, and educational databases to provide comprehensive information related to health and development. Data integration techniques, which identify records belonging to the same individual that reside in multiple data sets, are essential to these efforts. Several algorithms have been proposed in the literatures that are adept in integrating records from two different datasets. Our algorithms are aimed at integrating multiple (in particular more than two) datasets efficiently. Methods
Hierarchical clustering based solutions are used to integrate multiple (in particular more than two) datasets. Edit distance is used as the basic distance calculation, while distance calculation of common input errors is also studied. Several techniques have been applied to improve the algorithms in terms of both time and space: 1) Partial Construction of the Dendrogram (PCD) that ignores the level above the threshold; 2) Ignoring the Dendrogram Structure (IDS); 3) Faster Computation of the Edit Distance (FCED) that predicts the distance with the threshold by upper bounds on edit distance; and 4) A pre-processing blocking phase that limits dynamic computation within each block. Results
We have experimentally validated our algorithms on large simulated as well as real data. Accuracy and completeness are defined stringently to show the performance of our algorithms. In addition, we employ a four-category analysis. Comparison with FEBRL shows the robustness of our approach. Conclusions
In the experiments we conducted, the accuracy we observed exceeded 90% for the simulated data in most cases. 97.7% and 98.1% accuracy were achieved for the constant and proportional threshold, respectively, in a real dataset of 1,083,878 records
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
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