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227
On the Equivalence of Topological Relations
 International Journal of Geographical Information Systems
, 1995
"... Abstract. Analysis of global geographic phenomena requires nonplanar models. In the past, models for topological relations have focused either on a twodimensional or a threedimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the twodimensio ..."
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Cited by 113 (13 self)
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Abstract. Analysis of global geographic phenomena requires nonplanar models. In the past, models for topological relations have focused either on a twodimensional or a threedimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the twodimensional planar case, the eight binary topological relations between spatial regions are well known from the 9intersection model. This paper systematically develops the binary topological relations that can be realized on the surface of a sphere. Between two regions on the sphere there are three binary relations that cannot be realized in the plane. These relations complete the conceptual neighborhood graph of the eight planar topological relations in a regular fashion, providing evidence for a regularity of the underlying mathematical model. The analysis of the algebraic compositions of spherical topological relations indicates that spherical topological reasoning often provides fewer ambiguities than planar topological reasoning. Finally, a comparison with the relations that can be realized for onedimensional, ordered cycles draws parallels to the spherical topological relations. 1
The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
Logics for Hybrid Systems
 Proceedings of the IEEE
, 2000
"... This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems ..."
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Cited by 94 (7 self)
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This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems
Computing Minimum Length Paths of a Given Homotopy Class
 Comput. Geom. Theory Appl
, 1991
"... In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides reveal ..."
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Cited by 74 (7 self)
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In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides revealing connections between the minimum paths under these three distance functions, the framework provided by the universal cover leads to simplified lineartime algorithms for shortest path trees, for minimumlink paths in simple polygons, and for paths restricted to c given orientations. 1 Introduction If a wire, a pipe, or a robot must traverse a path among obstacles in the plane, then one might ask what is the best route to take. For the wire, perhaps the shortest distance is best; for the pipe, perhaps the fewest straightline segments. For the robot, either might be best depending on the relative costs of turning and moving. In this paper, we find shortest paths and shortest closed curve...
Convex partitions of polyhedra: a lower bound and worstcase optimal algorithm
 SIAM J. Comput
, 1984
"... Abstract. The problem of partitioning a polyhedron into aminimum number of convex pieces is known to be NPhard. We establish here a quadratic lower bound on the complexity of this problem, and we describe an algorithm that produces a number of convex parts within a constant factor of optimal in the ..."
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Cited by 68 (3 self)
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Abstract. The problem of partitioning a polyhedron into aminimum number of convex pieces is known to be NPhard. We establish here a quadratic lower bound on the complexity of this problem, and we describe an algorithm that produces a number of convex parts within a constant factor of optimal in the worst case. The algorithm is linear in the size of the polyhedron and cubic in the number of reflex angles. Since in most applications areas, the former quantity greatly exceeds the latter, the algorithm is viable in practice. Key words. Computational geometry, convex decompositions, data structures, lower bounds, polyhedra 1. Introduction. The
Approximating Polygons and Subdivisions with MinimumLink Paths
, 1991
"... We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate object ..."
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Cited by 60 (11 self)
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We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with no selfintersections are NPhard.
Hellytype theorems and generalized linear programming
 DISCRETE COMPUT. GEOM
, 1994
"... This thesis establishes a connection between the Helly theorems, a collection of results from combinatorial geometry, and the class of problems which we call Generalized Linear Programming, or GLP, which can be solved by combinatorial linear programming algorithms like the simplex method. We use the ..."
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Cited by 59 (0 self)
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This thesis establishes a connection between the Helly theorems, a collection of results from combinatorial geometry, and the class of problems which we call Generalized Linear Programming, or GLP, which can be solved by combinatorial linear programming algorithms like the simplex method. We use these results to explore the class GLP and show new applications to geometric optimization, and also to prove Helly theorems. In general, a GLP is a set...
The Behavior of Convolutional Codes
, 1995
"... It is well known that a convolutional code can be viewed as a linear system over a finite field. In this paper we develop this viewpoint for convolutional codes using several recent innovations from the systems theory literature. In particular we define codes as behaviors of a set of compact support ..."
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Cited by 47 (16 self)
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It is well known that a convolutional code can be viewed as a linear system over a finite field. In this paper we develop this viewpoint for convolutional codes using several recent innovations from the systems theory literature. In particular we define codes as behaviors of a set of compact support time trajectories over a vector space. We also consider several different representations of codes, in particular generalized first order representations. As an application of these ideas, we present a BCH construction technique for convolutional codes that yields optimal high rate codes.
A Canonical Model of the Region Connection Calculus
 Principles of Knowledge Representation and Reasoning: Proceedings of the 6th International Conference (KR98
, 1997
"... Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dimensio ..."
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Cited by 46 (6 self)
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Canonical models are very useful for determining simple representation formalism for qualitative relations. Allen's interval relations, e.g., can thereby be represented using the start and the end point of the intervals. Such a simple representation was not possible for regions of higher dimension as used by the Region Connection Calculus. In this paper we present a canonical model which allows regions and relations between them to be represented as points of the topological space and information about their neighbourhoods. With this formalism we are able to prove that whenever a set of RCC8 formulas is consistent there exists a realization in any dimension, even when the regions are constrained to be (sets of) polytopes. For three and higher dimensional space this is also true for internally connected regions. Using the canonical model we give algorithms for generating consistent scenarios. 1 Introduction The Region Connection Calculus (RCC) is a topological approach t...