## Delineating boundaries of imprecise regions (2005)

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Venue: | Proceedings of the EWCG |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Reinbacher05delineatingboundaries,

author = {Iris Reinbacher and Marc Benkert and Marc Van Kreveld and Joseph S. B. Mitchell and Er Wolff},

title = {Delineating boundaries of imprecise regions},

booktitle = {Proceedings of the EWCG},

year = {2005},

pages = {143--154}

}

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### Abstract

Abstract. In geographic information retrieval, queries often use names of geographic regions that do not have a well-defined boundary, such as “Southern France. ” We provide two classes of algorithms for the problem of computing reasonable boundaries of such regions, based on evidence of given data points that are deemed likely to lie either inside or outside the region. Our problem formulation leads to a number of problems related to red-blue point separation and minimum-perimeter polygons, many of which we solve algorithmically. We give experimental results from our implementation and a comparison of the two approaches. 1

### Citations

169 | On the shape of a set of points in the plane - Edelsbrunner, Kirkpatrick, et al. - 1983 |

164 | Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems
- Mitchell
- 1999
(Show Context)
Citation Context ...rates the bichromatic point set. This problem is NP-hard (by reduction from Euclidean traveling salesperson [6]); polynomial-time approximation schemes follow from the m-guillotine method of Mitchell =-=[10]-=- and from Arora’s method [3]. Minimum-link separation has also received attention [2]. In this paper we present two approaches to determine a reasonable polygon for a set of red and blue points. Based... |

131 |
Algorithms in Combinatorial Geometry, volume 10 of EATCS Monogr. Theoret. Comput. Sci
- Edelsbrunner
- 1987
(Show Context)
Citation Context ...ptation method, we start with a polygon P and adapt it until all blue points inside P are no longer inside, or the shape has to be changed too dramatically. By choosing P initially as an α-shape (see =-=[7]-=- for a definition), with α chosen such that e.g. 90% of the red points lie inside P , we can determine an appropriate initial shape and remove red outliers (red points outside P ) in the same step. Th... |

82 |
Linear-time algorithms for visibility and shortest path problems inside a triangulated simple polygon, Algorithmica 2
- Guibas, Hershberger, et al.
- 1987
(Show Context)
Citation Context ...= ∅. Middle: the case R �= ∅. Right: P ∗ for R �= ∅. Lemma 2. (i) The path F ∗ is a simple funnel. (ii) The base e of the funnel F ∗ is partially visible from b. We use the algorithm of Guibas et al. =-=[8]-=- to find the shortest path from the point b to every vertex v of the polygon. For every two adjacent vertices vi and vi+1 of the polygon, we compute the shortest paths connecting them to b. The algori... |

67 | Approximation algorithms for geometric tour and network design problems
- Mata, Mitchell
- 1995
(Show Context)
Citation Context ...e an O(n log n)-time algorithm that finds a polygon whose perimeter is at most O(log n) times as long as the minimum perimeter one. Separation by minimum link shapes received attention as well (e.g., =-=[10]-=-). In this paper we present two approaches to determine a reasonable polygon for a set of red and blue points. The first approach, described in Section 2, starts with a red polygon with blue points in... |

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- Purves, Ruas, et al.
- 2002
(Show Context)
Citation Context ...reases, so we get a linear number of recolorings. Theorem 7. The angle-and-degree recoloring algorithm requires O(n 2 log n) time. 4 Experiments In cooperation with our partners in the SPIRIT project =-=[9]-=- we got four data sets: Eastanglia (14, 57), Midlands (56, 52), Southeast (51, 49), and Wales (72, 54). The numbers in parentheses refer to the numbers of red and blue points in each data set, respect... |

56 |
Geographic Information Analysis
- O’Sullivan, Unwin
- 2002
(Show Context)
Citation Context ...h a polygon are: The red points are inside and the blue points are outside the polygon, which is simply connected and has small perimeter. Other shape measures for polygons that are used in geography =-=[12]-=-, e.g. the compactness ratio, can also be applied. In computational geometry, various red-blue separation algorithms exist; see [14] for a survey. Red-blue separation by a line can be solved by two-di... |

51 | Dynamic planar convex hull
- Brodal, Jacob
- 2002
(Show Context)
Citation Context ...lie between the right chains of F ∗ and F . We iterate through the h + 1 possible partitions that can lead to an optimal funnel F ∗ , and maintain the two chains using a dynamic convex-hull algorithm =-=[4]-=-. Every next pair of chains requires a deletion of a point on one chain and an insertion of the same point on the other chain. We maintain the length of the path during these updates to find the optim... |

45 | Low-dimensional linear programming with violations
- Chan
(Show Context)
Citation Context ...e separation by a line can be solved by two-dimensional linear programming in O(n) time for n points. Red-blue separation by a line with k misclassified points takes O((n + k 2 ) log k) expected time =-=[5]-=-. Other fixed separation shapes, e.g. strips, wedges, and sectors, have also been considered [14]. For polygonal separators, a natural choice is the minimum-perimeter polygon that separates the bichro... |

30 | A fast approximation algorithm for TSP with neighborhoods
- Gudmundsson, Levcopoulos
- 1999
(Show Context)
Citation Context ...is the minimum perimeter polygon that separates the bichromatic point set. Euclidean travelling salesperson can be reduced to this problem, which makes it intractable [5]. Gudmundsson and Levcopoulos =-=[7]-=- give an O(n log n)-time algorithm that finds a polygon whose perimeter is at most O(log n) times as long as the minimum perimeter one. Separation by minimum link shapes received attention as well (e.... |

21 | Web-based delineation of imprecise regions
- Arampatzis, Kreveld, et al.
- 2006
(Show Context)
Citation Context ...in similar sentence fragments, give locations that are not in the British Midlands. Details of using trigger phrases to determine locations inside or outside a region to be delineated can be found in =-=[1]-=-. Obviously the process is not very reliable, and false positives and false negatives are likely to occur. We have arrived at the following computational problem: given a set of “inside” points (red) ... |

21 |
Exploiting the Internet As a Geospatial Database
- Markowetz, Brinkho↵, et al.
- 2005
(Show Context)
Citation Context ...an imprecise region we can use the Web once again. The enormous amount of text on all Web pages can be used as a source of data; the idea of using the Web as a geo-spatial database appeared before in =-=[9, 11]-=-. A possible approach is using so-called trigger phrases. For any reasonable size city in the British Midlands, like Nottingham, it is quite likely that some Web page contains a sentence fragment like... |

13 | Approximation Schemes for Degree-Restricted MST and Red–Blue Separation Problems
- Arora, Chang
(Show Context)
Citation Context ...et. This problem is NP-hard (by reduction from Euclidean traveling salesperson [6]); polynomial-time approximation schemes follow from the m-guillotine method of Mitchell [10] and from Arora’s method =-=[3]-=-. Minimum-link separation has also received attention [2]. In this paper we present two approaches to determine a reasonable polygon for a set of red and blue points. Based on these approaches we defi... |

13 |
The complexity of computing minimum separating polygons
- Eades, Rappaport
- 1993
(Show Context)
Citation Context ... [14]. For polygonal separators, a natural choice is the minimum-perimeter polygon that separates the bichromatic point set. This problem is NP-hard (by reduction from Euclidean traveling salesperson =-=[6]-=-); polynomial-time approximation schemes follow from the m-guillotine method of Mitchell [10] and from Arora’s method [3]. Minimum-link separation has also received attention [2]. In this paper we pre... |

13 | Voronoibased region approximation for geographical information retrieval with gazetteers
- Alani, Jones, et al.
- 2001
(Show Context)
Citation Context ...de or outside a region to be delineated can be found in [2]. Obviously, the process is not too reliable and false positives and false negatives are likely to occur. In the reliable case, Alani et al. =-=[1]-=- give a Voronoi Diagram based method to delineate regions. We have arrived at the following computational problem: given a set of “inside” points (red) and a set of “outside” points (blue), determine ... |

11 |
Extracting spatial knowledge from the web
- Morimoto, Aono, et al.
- 2003
(Show Context)
Citation Context ...n imprecise region we can use the Web once again. The enormous amount of text on all Web pages can be used as a source of data; the idea of using the Web as a geo-spatial database has appeared before =-=[11]-=-. A possible approach is using so-called trigger phrases. For any reasonable-size city in the British Midlands, like Nottingham, it is quite likely that some Web page contains a sentence fragment like... |

11 |
On Geometric Separability
- Seara
- 2002
(Show Context)
Citation Context ...meter. Other shape measures for polygons that are used in geography [12], e.g. the compactness ratio, can also be applied. In computational geometry, various red-blue separation algorithms exist; see =-=[14]-=- for a survey. Red-blue separation by a line can be solved by two-dimensional linear programming in O(n) time for n points. Red-blue separation by a line with k misclassified points takes O((n + k 2 )... |

7 | Some separability problems in the plane
- Arkin, Hurtado, et al.
- 2000
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Citation Context ... misclassified points takes O((n + k 2 ) log k) expected time, where k is the number of misclassified points [4]. Other fixed separation shapes like strips, wedges, and sectors can also be considered =-=[3]-=-. When polygons are the separator, then the most natural problem is the minimum perimeter polygon that separates the bichromatic point set. Euclidean travelling salesperson can be reduced to this prob... |

1 |
Low-dimensionallinear programming with violations
- Chan
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Citation Context ... and takes O(n) time for n points. Red-blue separation by a line with the minimum number of misclassified points takes O((n + k 2 ) log k) expected time, where k is the number of misclassified points =-=[4]-=-. Other fixed separation shapes like strips, wedges, and sectors can also be considered [3]. When polygons are the separator, then the most natural problem is the minimum perimeter polygon that separa... |