Efficient incremental computation of attributes based on locally countable patterns in component trees

2016 ◽  
Author(s):  
Dennis J. Silva ◽  
Wonder A. L. Alves ◽  
Alexandre Morimitsu ◽  
Ronaldo F. Hashimoto
Keyword(s):  
Incremental Computation ◽  
Locally Countable

scholarly journals Incremental computation with names

2015 ◽  
Vol 50 (10) ◽  
pp. 748-766 ◽  
Author(s):  
Matthew A. Hammer ◽  
Joshua Dunfield ◽  
Kyle Headley ◽  
Nicholas Labich ◽  
Jeffrey S. Foster ◽  
...  
Keyword(s):  
Incremental Computation

On countably compact, locally countable spaces

1979 ◽  
Vol 10 (2-3) ◽  
pp. 193-206 ◽  
Author(s):  
I. Juhász ◽  
Zs. Nagy ◽  
W. Weiss
Keyword(s):  
Countably Compact ◽  
Locally Countable

Incremental Computation of Queries

2018 ◽  
pp. 1830-1833
Author(s):  
Guozhu Dong ◽  
Jianwen Su
Keyword(s):  
Incremental Computation

scholarly journals Distinguishability of Locally Finite Trees

10.37236/947 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Mark E. Watkins ◽  
Xiangqian Zhou
Keyword(s):  
Positive Integer ◽  
Chromatic Number ◽  
Inverse Image ◽  
Vertex Coloring ◽  
Finite Tree ◽  
Locally Finite ◽  
Distinguishing Number ◽  
Nonidentity Element ◽  
Locally Countable ◽  
Proper Vertex

The distinguishing number $\Delta(X)$ of a graph $X$ is the least positive integer $n$ for which there exists a function $f:V(X)\to\{0,1,2,\cdots,n-1\}$ such that no nonidentity element of $\hbox{Aut}(X)$ fixes (setwise) every inverse image $f^{-1}(k)$, $k\in\{0,1,2,\cdots,n-1\}$. All infinite, locally finite trees without pendant vertices are shown to be 2-distinguishable. A proof is indicated that extends 2-distinguishability to locally countable trees without pendant vertices. It is shown that every infinite, locally finite tree $T$ with finite distinguishing number contains a finite subtree $J$ such that $\Delta(J)=\Delta(T)$. Analogous results are obtained for the distinguishing chromatic number, namely the least positive integer $n$ such that the function $f$ is also a proper vertex-coloring.

ORBITS

2020 ◽  
Vol 14 (3) ◽  
pp. 294-306
Author(s):  
Mourad Khayati ◽  
Ines Arous ◽  
Zakhar Tymchenko ◽  
Philippe Cudré-Mauroux
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Multiple Time ◽  
Multiple Time Series ◽  
Online Data ◽  
Incremental Computation ◽  
Online Recovery ◽  
Recovery Technique ◽  
Centroid Decomposition

With the emergence of the Internet of Things (IoT), time series streams have become ubiquitous in our daily life. Recording such data is rarely a perfect process, as sensor failures frequently occur, yielding occasional blocks of data that go missing in multiple time series. These missing blocks do not only affect real-time monitoring but also compromise the quality of online data analyses. Effective streaming recovery (imputation) techniques either have a quadratic runtime complexity, which is infeasible for any moderately sized data, or cannot recover more than one time series at a time. In this paper, we introduce a new online recovery technique to recover multiple time series streams in linear time. Our recovery technique implements a novel incremental version of the Centroid Decomposition technique and reduces its complexity from quadratic to linear. Using this incremental technique, missing blocks are efficiently recovered in a continuous manner based on previous recoveries. We formally prove the correctness of our new incremental computation, which yields an accurate recovery. Our experimental results on real-world time series show that our recovery technique is, on average, 30% more accurate than the state of the art while being vastly more efficient.

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