scholarly journals Calculating the Optimal Step in Shift-Reduce Dependency Parsing: From Cubic to Linear Time

2019 ◽  
Vol 7 ◽  
pp. 283-296
Author(s):  
Mark-Jan Nederhof
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Ground Truth ◽  
Time Algorithm ◽  
Dependency Parsing ◽  
Projective Structures ◽  
Training Corpus

We present a new cubic-time algorithm to calculate the optimal next step in shift-reduce dependency parsing, relative to ground truth, commonly referred to as dynamic oracle. Unlike existing algorithms, it is applicable if the training corpus contains non-projective structures. We then show that for a projective training corpus, the time complexity can be improved from cubic to linear.

scholarly journals Global Greedy Dependency Parsing

2020 ◽  
Vol 34 (05) ◽  
pp. 8319-8326
Author(s):  
Zuchao Li ◽  
Hai Zhao ◽  
Kevin Parnow
Keyword(s):  
Feature Extraction ◽  
Polynomial Time ◽  
Time Complexity ◽  
Linear Time ◽  
Parse Tree ◽  
Dependency Parsing ◽  
Graph Models ◽  
Parse Trees ◽  
Left And Right ◽  
Syntactic Dependency

Most syntactic dependency parsing models may fall into one of two categories: transition- and graph-based models. The former models enjoy high inference efficiency with linear time complexity, but they rely on the stacking or re-ranking of partially-built parse trees to build a complete parse tree and are stuck with slower training for the necessity of dynamic oracle training. The latter, graph-based models, may boast better performance but are unfortunately marred by polynomial time inference. In this paper, we propose a novel parsing order objective, resulting in a novel dependency parsing model capable of both global (in sentence scope) feature extraction as in graph models and linear time inference as in transitional models. The proposed global greedy parser only uses two arc-building actions, left and right arcs, for projective parsing. When equipped with two extra non-projective arc-building actions, the proposed parser may also smoothly support non-projective parsing. Using multiple benchmark treebanks, including the Penn Treebank (PTB), the CoNLL-X treebanks, and the Universal Dependency Treebanks, we evaluate our parser and demonstrate that the proposed novel parser achieves good performance with faster training and decoding.

scholarly journals Constrained Arc-Eager Dependency Parsing

2014 ◽  
Vol 40 (2) ◽  
pp. 249-527 ◽  
Author(s):  
Joakim Nivre ◽  
Yoav Goldberg ◽  
Ryan McDonald
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Transition System ◽  
Dependency Graph ◽  
Dependency Parsing ◽  
Beam Search ◽  
Different Types

Arc-eager dependency parsers process sentences in a single left-to-right pass over the input and have linear time complexity with greedy decoding or beam search. We show how such parsers can be constrained to respect two different types of conditions on the output dependency graph: span constraints, which require certain spans to correspond to subtrees of the graph, and arc constraints, which require certain arcs to be present in the graph. The constraints are incorporated into the arc-eager transition system as a set of preconditions for each transition and preserve the linear time complexity of the parser.

scholarly journals A Linear Parallel Algorithm to Compute Bisimulation and Relational Coarsest Partitions

2021 ◽  
pp. 115-133
Author(s):  
Jan Martens ◽  
Jan Friso Groote ◽  
Lars van den Haak ◽  
Pieter Hijma ◽  
Anton Wijs
Keyword(s):  
Parallel Algorithm ◽  
Time Complexity ◽  
Linear Time ◽  
Random Access ◽  
Time Algorithm ◽  
Transition System ◽  
Linear Time Algorithm

AbstractThe most efficient way to calculate strong bisimilarity is by finding the relational coarsest partition of a transition system. We provide the first linear-time algorithm to calculate strong bisimulation using parallel random access machines (PRAMs). More precisely, with n states, m transitions and $$| Act |\le m$$ | A c t | ≤ m action labels, we provide an algorithm for $$\max (n,m)$$ max ( n , m ) processors that calculates strong bisimulation in time $$\mathcal {O}(n+| Act |)$$ O ( n + | A c t | ) and space $$\mathcal {O}(n+m)$$ O ( n + m ) . The best-known PRAM algorithm has time complexity $$\mathcal {O}(n\log n)$$ O ( n log n ) on a smaller number of processors making it less suitable for massive parallel devices such as GPUs. An implementation on a GPU shows that the linear time-bound is achievable on contemporary hardware.

scholarly journals Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 293
Author(s):  
Xinyue Liu ◽  
Huiqin Jiang ◽  
Pu Wu ◽  
Zehui Shao
Keyword(s):  
Linear Time ◽  
Minimum Weight ◽  
Domination Number ◽  
Time Algorithm ◽  
Simple Graph ◽  
Linear Time Algorithm ◽  
Domination Problem ◽  
Np Complete ◽  
Chordal Bipartite Graphs ◽  
Dominating Function

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

A Linear time algorithm for deciding security

1976 ◽  
Author(s):  
A. K. Jones ◽  
R. J. Lipton ◽  
L. Snyder
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm

AN IMPROVED ALGORITHM FOR FINDING TREE DECOMPOSITIONS OF SMALL WIDTH

2000 ◽  
Vol 11 (03) ◽  
pp. 365-371 ◽  
Author(s):  
LJUBOMIR PERKOVIĆ ◽  
BRUCE REED
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Tree Decomposition ◽  
Linear Time Algorithm ◽  
Input Graph ◽  
Primary Motivation ◽  
Small Width ◽  
Tree Decompositions ◽  
Improved Algorithm

We present a modification of Bodlaender's linear time algorithm that, for constant k, determine whether an input graph G has treewidth k and, if so, constructs a tree decomposition of G of width at most k. Our algorithm has the following additional feature: if G has treewidth greater than k then a subgraph G′ of G of treewidth greater than k is returned along with a tree decomposition of G′ of width at most 2k. A consequence is that the fundamental disjoint rooted paths problem can now be solved in O(n2) time. This is the primary motivation of this paper.

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