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Symmetric Word Alignments for Statistical Machine Translation
 In Proc. COLING
, 2004
"... In this paper, we address the word alignment problem for statistical machine translation. We aim at creating a symmetric word alignment allowing for reliable onetomany and manytoone word relationships. We perform the iterative alignment training in the sourcetotarget and the targettosource d ..."
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Cited by 38 (6 self)
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In this paper, we address the word alignment problem for statistical machine translation. We aim at creating a symmetric word alignment allowing for reliable onetomany and manytoone word relationships. We perform the iterative alignment training in the sourcetotarget and the targettosource direction with the wellknown IBM and HMM alignment models. Using these models, we robustly estimate the local costs of aligning a source word and a target word in each sentence pair. Then, we use efficient graph algorithms to determine the symmetric alignment with minimal total costs (i. e. maximal alignment probability). We evaluate the automatic alignments created in this way on the German–English Verbmobil task and the French–English Canadian Hansards task. We show statistically significant improvements of the alignment quality compared to the best results reported so far. On the Verbmobil task, we achieve an improvement of more than 1 % absolute over the baseline error rate of 4.7%. 1
PixeltoPixel Matching for Image Recognition Using Hungarian Graph Matching
 In DAGM 2004, Pattern Recognition, 26th DAGM Symposium
, 2004
"... A fundamental problem in image recognition is to evaluate the similarity of two images. This can be done by searching for the best pixeltopixel matching taking into account suitable constraints. In this paper, we present an extension of a zeroorder matching model called the image distortion model ..."
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Cited by 10 (6 self)
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A fundamental problem in image recognition is to evaluate the similarity of two images. This can be done by searching for the best pixeltopixel matching taking into account suitable constraints. In this paper, we present an extension of a zeroorder matching model called the image distortion model that yields stateoftheart classification results for di#erent tasks. We include the constraint that in the matching process each pixel of both compared images must be matched at least once. The optimal matching under this constraint can be determined using the Hungarian algorithm. The additional constraint leads to more homogeneous displacement fields in the matching. The method reduces the error rate of a nearest neighbor classifier on the well known USPS handwritten digit recognition task from 2.4% to 2.2%.
An O(n log n)time algorithm for the restriction scaffold assignment problem
 Journal of Computational Biology
"... The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n ..."
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Cited by 5 (3 self)
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The assignment problem takes as input two finite point sets S and T and establishes a correspondence between points in S and points in T, such that each point in S maps to exactly one point in T, and each point in T maps to at least one point in S. In this paper we show that this problem has an O(n log n)time solution, provided that the points in S and T are restricted to lie on a line (linear time, if S and T are presorted). 1
Efficient ManyToMany Point Matching in One Dimension
"... Let S and T be two sets of points with total cardinality n. The minimumcost manytomany matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both ..."
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Cited by 4 (0 self)
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Let S and T be two sets of points with total cardinality n. The minimumcost manytomany matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈ S to t ∈ T is equal to the distance between s and t. In this context, we provide an algorithm that determines a minimumcost manytomany matching in O(n log n) time, improving the previous best time complexity of O(n 2) for the same problem.
A Faster Algorithm for Computing the Link Distance between Two Point Sets on the Real Line
, 2005
"... Let S and T be point sets with S # T  and total cardinality n. A linking between S and T is a matching, L, between the sets where every element of S and T is matched to at least one element of the other set. The link distance is defined as the minimumcost linking. In this note we consider a s ..."
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Cited by 4 (1 self)
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Let S and T be point sets with S # T  and total cardinality n. A linking between S and T is a matching, L, between the sets where every element of S and T is matched to at least one element of the other set. The link distance is defined as the minimumcost linking. In this note we consider a special case of the link distance where both point sets lie on the real line and the cost of matching two points is the distance between them in the L 1 metric. An O(n ) algorithm for this problem is presented, improving the previous best known complexity of O(n ).
A Note on Packing Connectors
, 1997
"... Given an undirected graph G = (V; E) and a partition fS; Tg of V , an ST connector is a set of edges F ` E such that every component of the subgraph (V; F ) intersects both S and T . We show that G has k edgedisjoint ST connectors if and only if jffi G (V 1 ) [ : : : [ ffi G (V t )j kt for every ..."
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Given an undirected graph G = (V; E) and a partition fS; Tg of V , an ST connector is a set of edges F ` E such that every component of the subgraph (V; F ) intersects both S and T . We show that G has k edgedisjoint ST connectors if and only if jffi G (V 1 ) [ : : : [ ffi G (V t )j kt for every collection fV 1 ; : : : ; V t g of disjoint nonempty subsets of S and for every such collection of subsets of T . This is a common generalization of a theorem of Tutte and NashWilliams on disjoint spanning trees and a theorem of König on disjoint edge covers in a bipartite graph.