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Labeled trees and the efficient computation of derivations

R. Grossman, R. G. Larson
1989 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89  
Since 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.  ... 
doi:10.1145/74540.74550 dblp:conf/issac/GrossmanL89 fatcat:yamivbtimfbrjmfkxvx6bps7bu

Optree: A Learning-Based Adaptive Watershed Algorithm for Neuron Segmentation [chapter]

Mustafa Gökhan Uzunbaş, Chao Chen, Dimitris Metaxsas
2014 Lecture Notes in Computer Science  
Our algorithm outperforms state-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.  ... 
doi:10.1007/978-3-319-10404-1_13 fatcat:r4re2phkivgdfcfdjgkdctsgsi

The explicit computation of integration algorithms and first integrals for ordinary differential equations with polynomial coefficients using trees

P. E. Crouch, R. L. Grossman
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.  ... 
doi:10.1145/143242.143277 dblp:conf/issac/CrouchG92 fatcat:iymszws3p5flpejuj5incjcwca

LR recursive transition networks for Earley and Tomita parsing

Mark Perlin
1991 Proceedings of the 29th annual meeting on Association for Computational Linguistics -  
At most, this is 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.  ... 
doi:10.3115/981344.981357 dblp:conf/acl/Perlin91 fatcat:du3jw2dv2jg4vipac66sweah3a

An efficient conditional random field approach for automatic and interactive neuron segmentation

Mustafa Gokhan Uzunbas, Chao Chen, Dimitris Metaxas
2016 Medical Image Analysis  
Our algorithm outperforms state-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  ... 
doi:10.1016/j.media.2015.06.003 pmid:26210001 fatcat:vuolpfytq5gqdpoofwn2kb2twy

Symbolic computation of derivations using labelled trees

Robert Grossman, Richard G. Larson
1992 Journal of symbolic computation  
We discuss 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.  ... 
doi:10.1016/s0747-7171(10)80009-4 fatcat:z2lwhmcybjcxdfg55iiprtvvgq

An Omission-Tolerant Cryptographic Checksum [article]

Francisco Corella, Karen Pomian Lewison
2019 IACR Cryptology ePrint Archive  
To 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  ... 
dblp:journals/iacr/CorellaL19 fatcat:4kugy5gsuff4diz7drsmjelnq4

Secure Key-Updating for Lazy Revocation [chapter]

Michael Backes, Christian Cachin, Alina Oprea
2006 Lecture Notes in Computer Science  
Finally, we give a systematic analysis 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).  ... 
doi:10.1007/11863908_21 fatcat:3jkngcubcjgkzc6t2ge66ee3dm

TAL Recognition inO(M(n2)) Time

Sanguthevar Rajasekaran, Shibu Yooseph
1998 Journal of computer and system sciences (Print)  
We propose an O(M(n 2 )) time algorithm for 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.  ... 
doi:10.1006/jcss.1997.1537 fatcat:ucdyiafhyrghfbhrjirxm4kxva

Efficient LZ78 Factorization of Grammar Compressed Text [chapter]

Hideo Bannai, Shunsuke Inenaga, Masayuki Takeda
2012 Lecture Notes in Computer Science  
Given an SLP 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.  ... 
doi:10.1007/978-3-642-34109-0_10 fatcat:zs474qki75denpbcfiwpi5rp34

A Classification-Segmentation Framework for the Detection of Individual Trees in Dense MMS Point Cloud Data Acquired in Urban Areas

Martin Weinmann, Michael Weinmann, Clément Mallet, Mathieu Brédif
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  ... 
doi:10.3390/rs9030277 fatcat:hxqvk6mcenaafbmicotv45dgfu

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

Xuezhe Ma, Eduard Hovy
2015 Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing  
In this paper, we proposed an 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.  ... 
doi:10.18653/v1/d15-1154 dblp:conf/emnlp/MaH15 fatcat:ulkasnaol5a4jjfdxy4r7y4xhq

Multi-label Classification without the Multi-label Cost [chapter]

Xiatian Zhang, Quan Yuan, Shiwan Zhao, Wei Fan, Wentao Zheng, Zhong Wang
2010 Proceedings of the 2010 SIAM International Conference on Data Mining  
We formally analyze 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.  ... 
doi:10.1137/1.9781611972801.68 dblp:conf/sdm/ZhangYZFZW10 fatcat:peugf5d7irh4xpofe4snecue2i

Efficient Label Encoding for Range-Based Dynamic XML Labeling Schemes [chapter]

Liang Xu, Tok Wang Ling, Zhifeng Bao, Huayu Wu
2010 Lecture Notes in Computer Science  
We point out 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.  ... 
doi:10.1007/978-3-642-12026-8_21 fatcat:ay6zxc2p3ndt5f2su25xiryhqq

Generation as dependency parsing

Alexander Koller, Kristina Striegnitz
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 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.  ... 
doi:10.3115/1073083.1073088 dblp:conf/acl/KollerS02 fatcat:itnjzytbs5ca5fu6nj2phol4ha
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