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Voronoi diagrams  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
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Cited by 753 (5 self)
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This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.
Ambivalent data structures for dynamic 2edgeconnectivity and k smallest spanning trees
 In 32nd Annual Symposium on Foundations of Computer Science FOCS
, 1991
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Improved Sparsification
, 1993
"... In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using ..."
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Cited by 29 (5 self)
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In previous work we introduced sparsification, a technique that transforms fully dynamic algorithms for sparse graphs into ones that work on any graph, with a logarithmic increase in complexity. In this work we describe an improvement on this technique that avoids the logarithmic overhead. Using our improved sparsification technique, we keep track of the following properties: minimum spanning forest, best swap, connectivity, 2edgeconnectivity, and bipartiteness, in time O(n 1/2 ) per edge insertion or deletion; 2vertexconnectivity and 3vertexconnectivity, in time O(n) per update; and 4vertexconnectivity, in time O(n#(n)) per update.
Discriminative Learning and Spanning Tree Algorithms for Dependency Parsing
, 2006
"... In this thesis we develop a discriminative learning method for dependency parsing using
online largemargin training combined with spanning tree inference algorithms. We will
show that this method provides stateoftheart accuracy, is extensible through the feature
set and can be implemented effici ..."
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Cited by 23 (1 self)
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In this thesis we develop a discriminative learning method for dependency parsing using
online largemargin training combined with spanning tree inference algorithms. We will
show that this method provides stateoftheart accuracy, is extensible through the feature
set and can be implemented efficiently. Furthermore, we display the language independent
nature of the method by evaluating it on over a dozen diverse languages as well as show its
practical applicability through integration into a sentence compression system.
We start by presenting an online largemargin learning framework that is a generaliza
tion of the work of Crammer and Singer [34, 37] to structured outputs, such as sequences
and parse trees. This will lead to the heart of this thesis – discriminative dependency pars
ing. Here we will formulate dependency parsing in a spanning tree framework, yielding
efficient parsing algorithms for both projective and nonprojective tree structures. We will
then extend the parsing algorithm to incorporate features over larger substructures with
out an increase in computational complexity for the projective case. Unfortunately, the
nonprojective problem then becomes NPhard so we provide structurally motivated ap
proximate algorithms. Having defined a set of parsing algorithms, we will also define a
rich feature set and train various parsers using the online largemargin learning framework.
We then compare our trained dependency parsers to other stateoftheart parsers on 14
diverse languages: Arabic, Bulgarian, Chinese, Czech, Danish, Dutch, English, German,
Japanese, Portuguese, Slovene, Spanish, Swedish and Turkish.
Having built an efficient and accurate discriminative dependency parser, this thesis will
then turn to improving and applying the parser. First we will show how additional re
sources can provide useful features to increase parsing accuracy and to adapt parsers to
new domains. We will also argue that the robustness of discriminative inferencebased
learning algorithms lend themselves well to dependency parsing when feature representa
tions or structural constraints do not allow for tractable parsing algorithms. Finally, we
integrate our parsing models into a stateoftheart sentence compression system to show
its applicability to a real world problem.
A Linear Algorithm for Analysis of Minimum Spanning and Shortest Path Trees of Planar Graphs
 Algorithmica
, 1992
"... We give a linear time and space algorithm for analyzing trees in planar graphs. The algorithm can be used to analyze the sensitivity of a minimum spanning tree to changes in edge costs, to find its replacement edges, and to verify its minimality. It can also be used to analyze the sensitivity of a s ..."
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Cited by 17 (0 self)
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We give a linear time and space algorithm for analyzing trees in planar graphs. The algorithm can be used to analyze the sensitivity of a minimum spanning tree to changes in edge costs, to find its replacement edges, and to verify its minimality. It can also be used to analyze the sensitivity of a singlesource shortest path tree to changes in edge costs, and to analyze the sensitivity of a minimum cost network flow. The algorithm is simple and practical. It uses the properties of a planar embedding, combined with a heapordered queue data structure. Let G = (V; E) be a planar graph, either directed or undirected, with n vertices and m = O(n) edges. Each edge e 2 E has a realvalued cost cost(e). A minimum spanning tree of a connected, undirected planar graph G is a spanning tree of minimum total edge cost. If G is directed and r is a vertex from which all other vertices are reachable, then a shortest path tree from r is a spanning tree that contains a minimumcost path from r to every...
Offline Algorithms for Dynamic Minimum Spanning Tree Problems
, 1994
"... We describe an efficient algorithm for maintaining a minimum spanning tree (MST) in a graph subject to a sequence of edge weight modifications. The sequence of minimum spanning trees is computed offline, after the sequence of modifications is known. The algorithm performs O(log n) work per modificat ..."
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Cited by 17 (8 self)
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We describe an efficient algorithm for maintaining a minimum spanning tree (MST) in a graph subject to a sequence of edge weight modifications. The sequence of minimum spanning trees is computed offline, after the sequence of modifications is known. The algorithm performs O(log n) work per modification, where n is the number of vertices in the graph. We use our techniques to solve the offline geometric MST problem for a planar point set subject to insertions and deletions; our algorithm for this problem performs O(log 2 n) work per modification. No previous dynamic geometric MST algorithm was known.
The CP(Graph) Computation Domain in Constraint Programming
, 2006
"... Dissertation présentée en vue de l’obtention du titre de Docteur en ..."
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Cited by 5 (0 self)
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Dissertation présentée en vue de l’obtention du titre de Docteur en
Spanning Tree Methods for Discriminative Training of Dependency Parsers
"... Untyped dependency parsing can be viewed as the problem of finding maximum spanning trees (MSTs) in directed graphs. Using this representation, the Eisner (1996) parsing algorithm is sufficient for searching the space of projective trees. More importantly, the representation is extended naturally to ..."
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Cited by 4 (0 self)
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Untyped dependency parsing can be viewed as the problem of finding maximum spanning trees (MSTs) in directed graphs. Using this representation, the Eisner (1996) parsing algorithm is sufficient for searching the space of projective trees. More importantly, the representation is extended naturally to nonprojective parsing using ChuLiuEdmonds (Chu and Liu, 1965; Edmonds, 1967) MST algorithm. These efficient parse search methods support largemargin discriminative training methods for learning dependency parsers. We evaluate these methods experimentally on the English and Czech treebanks. 1
Graph Modeling of Metabolism
, 2000
"... This paperpro oo the graphmo delingo metab It is po]F)j8 to describe metab otab as acirculatio o atoc by representing allreactio] with the chemical structureso smallcol oll (metaboetab8# Enzymatic reactioc are regarded as the rearrangement o chemicals, and the mappinginfog8#)Fx o atoo between struct ..."
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Cited by 4 (0 self)
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This paperpro oo the graphmo delingo metab It is po]F)j8 to describe metab otab as acirculatio o atoc by representing allreactio] with the chemical structureso smallcol oll (metaboetab8# Enzymatic reactioc are regarded as the rearrangement o chemicals, and the mappinginfog8#)Fx o atoo between structures arestoF# in a database. In fact, the tracer experiment inbio chemistry is basedo thismo del,altho:# the mappinginfog8FCx) is referenced with the traditiodj metabota mapo paper. This tracinge#oi shoin be minimized by the digitizatio o metab otab as in o8pro ject. 2 Method andResul
CNOP: a package for constrained network optimization
 IN PROC. 3RD INT. WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS (ALENEX 01), LNCS 2153
, 2001
"... We present a generic package for resource constrained network optimization problems. We illustrate the flexibility and the use of our package by solving four applications: route planning, curve approximation, minimum cost reliability constrained spanning trees and the table layout problem. ..."
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Cited by 4 (0 self)
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We present a generic package for resource constrained network optimization problems. We illustrate the flexibility and the use of our package by solving four applications: route planning, curve approximation, minimum cost reliability constrained spanning trees and the table layout problem.