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Labeled trees and the efficient computation of derivations

1989
*
Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89
*

Since

doi:10.1145/74540.74550
dblp:conf/issac/GrossmanL89
fatcat:yamivbtimfbrjmfkxvx6bps7bu
*the*set*of**labeled**trees*form a basis for k{LT (E 1 , . . . , E M )}, it is sufficient to describe*the*product*of*two*labeled**trees*. Suppose t 1*and*t 2 are two*labeled**trees*. ... Proposition 7 Let σ = φ(p),*and*denote by |σ|*the*number*of**labeled**trees*with non-zero coefficients in σ. Then*the*cost*of**computing*ψ(σ) is 2m|σ|N m . ... We assume that there is one processor available for each*labeled**tree*which arises in*the**computation*. LabelIndex is defined to be an index taking values between 1*and*m. ...##
###
Optree: A Learning-Based Adaptive Watershed Algorithm for Neuron Segmentation
[chapter]

2014
*
Lecture Notes in Computer Science
*

Our algorithm outperforms state-

doi:10.1007/978-3-319-10404-1_13
fatcat:r4re2phkivgdfcfdjgkdctsgsi
*of*-*the*-art methods. Both*the*inference*and**the*training are very*efficient*as*the*graph is*tree*-structured. ...*The*uncertainty is measured by*the*marginals*of**the*graphical model. Based on user corrections, our framework modifies*the*merging*tree**and*thus improves*the*segmentation globally. ...*The*correspondence between*tree*-*derived*segmentations*and**the**labelings**of*T is provided as follows. ...##
###
The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees

1992
*
Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92
*

*The*

*derivation*

*of*specialized numerical algorithms,

*the*explicit symbolic

*computation*

*of*integrals

*of*motion,

*and*

*the*explicit

*computation*

*of*normal forms for nonlinear systems all require such

*computations*...

*The*basic idea is to impose a multiplicative structure on

*the*vector space with basis

*the*set

*of*finite rooted

*trees*

*and*whose nodes are

*labeled*with

*the*coefficients

*of*

*the*differential operators. ... Note that ψ(σ) is 0, if

*the*

*tree*σ contains a node

*labeled*x which has two or more children

*labeled*with b, c, . . . representing one

*of*

*the*

*derivations*. ...

##
###
LR recursive transition networks for Earley and Tomita parsing

1991
*
Proceedings of the 29th annual meeting on Association for Computational Linguistics -
*

At most, this is

doi:10.3115/981344.981357
dblp:conf/acl/Perlin91
fatcat:du3jw2dv2jg4vipac66sweah3a
*the*set SAME-*LABEL*(rule) = { N • RTN I N is a symbol node,*and**the**label**of*N is identical to*the**label**of**the*rule's nonterminal successor node }. ... INTRODUCTION Ambiguous context-free grammars (CFGs) are currently used in*the*syntactic*and*semantic processing*of*natural language. For*efficient*parsing, two major*computational*methods are used. ...##
###
An efficient conditional random field approach for automatic and interactive neuron segmentation

2016
*
Medical Image Analysis
*

Our algorithm outperforms state-

doi:10.1016/j.media.2015.06.003
pmid:26210001
fatcat:vuolpfytq5gqdpoofwn2kb2twy
*of*-*the*-art methods. Both*the*inference*and**the*training are very*efficient*as*the*graph is*tree*-structured. ... However, with data sets this size, manual analysis is no longer feasible.This challenges 23*the**computer*vision*and*machine learning community to develop accurate*and**efficient*techniques 24 for neuron ... We call such segmentations*tree*-*derived**and*our algorithm search through*the*space 185*of*all T -*derived*segmentations, denoted by S T ⊆ S. 186*The*correspondence between*tree*-*derived*segmentations*and*...##
###
Symbolic computation of derivations using labelled trees

1992
*
Journal of symbolic computation
*

We discuss

doi:10.1016/s0747-7171(10)80009-4
fatcat:z2lwhmcybjcxdfg55iiprtvvgq
*the*effective symbolic*computation**of*operators under composition. We analyse data structures consisting*of*formal linear combinations*of*rooted*labelled**trees*. ... This leads to an algorithm which, for operators which are*derivations*, speeds up*the**computation*exponentially in*the*degree*of**the*operator. ... We conclude this section with a simple example*of*a*computation**of*a third order*derivation*using*trees*. Fix*the**derivations*N E j = L afD IL , IL=·*and*consider*the*higher order*derivation*p =E JE2E. ...##
###
An Omission-Tolerant Cryptographic Checksum
[article]

2019
*
IACR Cryptology ePrint Archive
*

To

dblp:journals/iacr/CorellaL19
fatcat:4kugy5gsuff4diz7drsmjelnq4
*compute**the*checksum on*the*encoding we deserialize*the*bitstring,*compute**the*missing internal nodes,*and*output*the**label**of**the*root node as*the*checksum. ... To do so, we encode each key-value pair as*the*type*and**label**of*a leaf node*of*an incomplete typed hash*tree*without internalnode*labels*, then serialize*the**tree*to obtain a bit-string encoding*of**the*... To prove that Y satisfies one*of**the*conditions (i), (ii) or (iii)*of**the*theorem we consider*the**computation**of**the*internal*labels**of**the*nodes*of*Y , X,*and*various pruned*derivatives**of*X using Algorithm ...##
###
Secure Key-Updating for Lazy Revocation
[chapter]

2006
*
Lecture Notes in Computer Science
*

Finally, we give a systematic analysis

doi:10.1007/11863908_21
fatcat:3jkngcubcjgkzc6t2ge66ee3dm
*of**the**computational**and*communication complexity*of**the*three constructions*and*show that*the*novel construction improves*the*previously known constructions. ... We consider*the*problem*of**efficient*key management*and*user revocation in cryptographic file systems that allow shared access to files. ...*the**label**and**the**tree*-key*of**the*left sibling*of**the*node with*label*ℓ (assuming*the**labels**and**tree*-keys*of**the*siblings are in A). ...##
###
TAL Recognition inO(M(n2)) Time

1998
*
Journal of computer and system sciences (Print)
*

We propose an O(M(n 2 )) time algorithm for

doi:10.1006/jcss.1997.1537
fatcat:ucdyiafhyrghfbhrjirxm4kxva
*the*recognition*of**tree*adjoining languages (TALs), where n is*the*size*of**the*input string*and*M(k) is*the*time needed to multiply two k_k boolean matrices. ...*Tree*adjoining grammars are formalisms suitable for natural language processing*and*have received enormous attention in*the*past among not only natural language processing researchers but also algorithms ... Informally, each edge in this*derivation**tree*is*labelled*with*the*address*of**the*node where*the*auxiliary*tree*, indicated by*the**label*on*the*lower vertex*of*this edge, is adjoined. ...##
###
Efficient LZ78 Factorization of Grammar Compressed Text
[chapter]

2012
*
Lecture Notes in Computer Science
*

Given an SLP

doi:10.1007/978-3-642-34109-0_10
fatcat:zs474qki75denpbcfiwpi5rp34
*of*size n representing a text S*of*length N, our algorithm*computes**the*LZ78 factorization*of*T in O(n√(N)+m N) time*and*O(n√(N)+m) space, where m is*the*number*of*resulting LZ78 factors. ... We present an*efficient*algorithm for*computing**the*LZ78 factorization*of*a text, where*the*text is represented as a straight line program (SLP), which is a context free grammar in*the*Chomsky normal form ... Acknowledgements We thank*the*anonymous reviewers for helpful comments to improve*the*paper. ...##
###
A Classification-Segmentation Framework for the Detection of Individual Trees in Dense MMS Point Cloud Data Acquired in Urban Areas

2017
*
Remote Sensing
*

*The*

*derived*results clearly reveal a semantic classification

*of*high accuracy (up to 90.77%)

*and*an instance-level segmentation

*of*high plausibility, while

*the*simplicity, applicability

*and*

*efficiency*... 3D points, whereby

*the*

*labels*are defined as "

*tree*points"

*and*"other points". ... This is followed by a discussion

*of*

*the*

*derived*results with respect to accuracy, robustness

*and*

*efficiency*(Section 5)

*and*a summary

*of*

*the*strengths

*and*limitations

*of*our framework

*and*

*the*involved ...

##
###
Efficient Inner-to-outer Greedy Algorithm for Higher-order Labeled Dependency Parsing

2015
*
Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing
*

In this paper, we proposed an

doi:10.18653/v1/d15-1154
dblp:conf/emnlp/MaH15
fatcat:ulkasnaol5a4jjfdxy4r7y4xhq
*efficient*dependency parsing algorithm that is capable*of*capturing multiple edge-*label*features, while maintaining low*computational*complexity. ... Our parser consistently obtains more accurate results than three baseline systems*and*three popular, off-*the*-shelf parsers. ... Any opinions, findings,*and*conclusions or recommendations expressed in this material are those*of**the*authors*and*do not necessarily reflect*the*views*of*DARPA. ...##
###
Multi-label Classification without the Multi-label Cost
[chapter]

2010
*
Proceedings of the 2010 SIAM International Conference on Data Mining
*

We formally analyze

doi:10.1137/1.9781611972801.68
dblp:conf/sdm/ZhangYZFZW10
fatcat:peugf5d7irh4xpofe4snecue2i
*the*learning risk*of*Random Decision*Tree*(RDT)*and**derive*that*the*upper bound*of*risk is stable*and*lower bound decreases as*the*number*of**trees*increases. ... Experiment results have demonstrated that*the**computation*time*of**the*proposed approaches is 1-3 orders*of*magnitude less than other methods when handling datasets with large number*of*instances*and**labels*... Unauthorized reproduction*of*this article is prohibited. ...##
###
Efficient Label Encoding for Range-Based Dynamic XML Labeling Schemes
[chapter]

2010
*
Lecture Notes in Computer Science
*

We point out

doi:10.1007/978-3-642-12026-8_21
fatcat:ay6zxc2p3ndt5f2su25xiryhqq
*the*problems*of*existing encoding algorithms which include*computational**and*memory inefficiencies. ... We show that ST encoding is widely applicable to different dynamic*labels**and*prove*the*optimality*of*our results. ... By partitioning*the*range to be encoded, we can re-use some*of**the*previously-*computed*mappings*and*avoid re-*computing*g for*the*whole range. ...##
###
Generation as dependency parsing

2001
*
Proceedings of the 40th Annual Meeting on Association for Computational Linguistics - ACL '02
*

This makes it necessary to develop algorithms that run with reasonable

doi:10.3115/1073083.1073088
dblp:conf/acl/KollerS02
fatcat:itnjzytbs5ca5fu6nj2phol4ha
*efficiency*in practice despite*the*high worstcase complexity. ... We show how to convert TAG generation problems into dependency parsing problems, which is useful because optimizations in recent dependency parsers based on constraint programming tackle exactly*the*combinatorics ... We are grateful to Tilman Becker, Chris Brew, Ann Copestake, Ralph Debusmann, Gerald Penn, Stefan Thater,*and*our reviewers for helpful comments*and*discussions. ...
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