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13
Distance Measures for Point Sets and Their Computation
 Acta Informatica
, 1997
"... We consider the problem of measuring the similarity or distance between two finite sets of points in a metric space, and computing the measure. This problem has applications in, e.g., computational geometry, philosophy of science, updating or changing theories, and machine learning. We review some o ..."
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Cited by 50 (2 self)
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We consider the problem of measuring the similarity or distance between two finite sets of points in a metric space, and computing the measure. This problem has applications in, e.g., computational geometry, philosophy of science, updating or changing theories, and machine learning. We review some of the distance functions proposed in the literature, among them the minimum distance link measure, the surjection measure, and the fair surjection measure, and supply polynomial time algorithms for the computation of these measures. Furthermore, we introduce the minimum link measure, a new distance function which is more appealing than the other distance functions mentioned. We also present a polynomial time algorithm for computing this new measure. We further address the issue of defining a metric on point sets. We present the metric infimum method that constructs a metric from any distance functions on point sets. In particular, the metric infimum of the minimum link measure is a quite int...
A Polynomial Time Computable Metric Between Point Sets
, 2000
"... Measuring the similarity or distance between two sets of points in a metric space is an important problem in machine learning and has also applications in other disciplines e.g. in computational geometry, philosophy of science, methods for updating or changing theories, . . . . Recently Eiter and Ma ..."
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Cited by 40 (3 self)
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Measuring the similarity or distance between two sets of points in a metric space is an important problem in machine learning and has also applications in other disciplines e.g. in computational geometry, philosophy of science, methods for updating or changing theories, . . . . Recently Eiter and Mannila have proposed a new measure which is computable in polynomial time. However, it is not a distance function in the mathematical sense because it does not satisfy the triangle inequality.
A Framework for Defining Distances Between FirstOrder Logic Objects
, 1998
"... this paper we develop a framework for distances between clauses and distances between models. The framework can be parametrised by a measure for the distance between atoms. It takes into account subterms common to distinct atoms of a set of atoms in the measurement of the distance between sets. More ..."
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Cited by 30 (3 self)
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this paper we develop a framework for distances between clauses and distances between models. The framework can be parametrised by a measure for the distance between atoms. It takes into account subterms common to distinct atoms of a set of atoms in the measurement of the distance between sets. Moreover, for a constant number of variables, the complexity of the distance computation is polynomially bounded by the size of the objects. Initial experiments show that the framework can be the basis of good clustering algorithms. The framework consists of three levels: At the first level one chooses a distance between atoms . The second level upgrades this distance to a distance between sets of atoms. We propose a framework that is a generalisation of three polynomial time computable similarity measures proposed by Eiter and Mannila, and an instance which is a real distance function, computable in polynomial time. We develop also a binary prototype function for sets of points. Prototype fun
Online Graph Algorithms for Incremental Compilation
, 1992
"... Compilers usually construct various data structures which often vary only slightly fi'om compilation run to compilation run. This paper gives various solutions to the problems of quickly updating these data structures instead of building them from scratch each time. All problems we found can be redu ..."
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Cited by 19 (0 self)
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Compilers usually construct various data structures which often vary only slightly fi'om compilation run to compilation run. This paper gives various solutions to the problems of quickly updating these data structures instead of building them from scratch each time. All problems we found can be reduced to graph problems. Specifically, we give algorithms for updating data structures for the problems of topological order, loop detection, and reachability from the start routine.
Discrete Loops and Worst Case Performance
 Computer Languages
, 1994
"... In this paper socalled discrete loops are introduced which narrow the gap between general loops (e.g. while or repeatloops) and forloops. Alt hough discrete loops can be used for applications that would otherwise require general loops, discrete loops are known to complete in any case. Furthe ..."
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Cited by 15 (7 self)
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In this paper socalled discrete loops are introduced which narrow the gap between general loops (e.g. while or repeatloops) and forloops. Alt hough discrete loops can be used for applications that would otherwise require general loops, discrete loops are known to complete in any case. Furthermore it is possible to determine the number of iterations of a discrete loop, while this is trivial to do for forloops and extremely difficult for general loops. Thus discrete loops form an ideal framework for determining the worst case timing behavior of a program and they are especially useful in implementing realtime systems and proving such systems correct.
Fast FixedParameter Tractable Algorithms for Nontrivial Generalizations of Vertex Cover
, 2003
"... Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider ..."
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Cited by 12 (0 self)
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Our goal in this paper is the development of fast algorithms for recognizing general classes of graphs. We seek algorithms whose complexity can be expressed as a linear function of the graph size plus an exponential function of k, a natural parameter describing the class. In particular, we consider the class W_k(G), where for each graph G in W_k(G), the removal of a set of at most k vertices from G results in a graph in the base graph class G. (If G ist the class of edgeless graphs,...
WorstCase Space and Time Complexity of Recursive Procedures
"... The purpose of this paper is to show that recursive procedures can be used for implementing realtime applications without harm, if a few conditions are met. These conditions ensure that upper bounds for space and time requirements can be derived at compile time. Moreover they are simple enough such ..."
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Cited by 10 (4 self)
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The purpose of this paper is to show that recursive procedures can be used for implementing realtime applications without harm, if a few conditions are met. These conditions ensure that upper bounds for space and time requirements can be derived at compile time. Moreover they are simple enough such that many important recursive algorithms can be implemented, for example Mergesort or recursive treetraversal algorithms. In addition,
Relational IBL in music with a new structural similarity measure
 In Proceedings of the International Conference on Inductive Logic Programming
, 2003
"... Abstract. It is well known that many hard tasks considered in machine learning and data mining can be solved in an rather simple and robust way with an instance and distancebased approach. In this paper we present another difficult task: learning, from large numbers of performances by concert pian ..."
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Cited by 8 (2 self)
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Abstract. It is well known that many hard tasks considered in machine learning and data mining can be solved in an rather simple and robust way with an instance and distancebased approach. In this paper we present another difficult task: learning, from large numbers of performances by concert pianists, to play music expressively. We model the problem as a multilevel decomposition and prediction task. Motivated by structural characteristics of such a task, we propose a new relational distance measure that is a rather straightforward combination of two existing measures. Empirical evaluation shows that our approach is in general viable and our algorithm, named DISTALL, is indeed able to produce musically interesting results. The experiments also provide evidence of the success of ILP in a complex domain such as music performance: it is shown that our instancebased learner operating on structured, relational data outperforms a propositional kNN algorithm.
On the Performance of Networks with Multiple Busses
 Proceedings of Symposion on Theoretical Aspects of Computer Science (STACS '92), volume 577 of LNCS
, 1991
"... We address the following questions: 1) To which extend can the computation power of parallel processor networks be increased by using busses, i.e. by providing broadcast facilities in the networks? 2) To which extend can shared memory cells of PRAMs be replaced by links? (For this question, note ..."
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Cited by 6 (0 self)
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We address the following questions: 1) To which extend can the computation power of parallel processor networks be increased by using busses, i.e. by providing broadcast facilities in the networks? 2) To which extend can shared memory cells of PRAMs be replaced by links? (For this question, note that a shared memory cell can be viewed as a global bus.) We show upper and lower bounds for computing commutative associative operations such as ADDITION or MAXIMUM on networks with busses. Our bounds are based on simple graph theoretical properties of the networks. As to question 1, these results demonstrate that busses can increase the performance of networks with large diameter. For example, computing MAXIMUM on a ddimensional mesh with N processors needs time \Theta( d p N ) without busses, but only time \Theta i d+1 q N m + log log N j with m CRCWbusses. As to question 2, these results demonstrate that the storage requirement of optimal PRAM algorithms can be reduc...