Algorithms — ESA 2002: 10th Annual European Symposium Rome, by William Cook (auth.), Rolf Möhring, Rajeev Raman (eds.)

By William Cook (auth.), Rolf Möhring, Rajeev Raman (eds.)

This quantity includes the seventy four contributed papers and abstracts of four of the five invited talks provided on the tenth Annual eu Symposium on Algorithms (ESA 2002), held on the college of Rome “La Sapienza”, Rome, Italy, 17-21 September, 2002. For the ?rst time, ESA had tracks, with separate application committees, which dealt respectively with: – the layout and mathematical research of algorithms (the “Design and An- ysis” track); – real-world purposes, engineering and experimental research of algorithms (the “Engineering and functions” track). past ESAs have been held in undesirable Honnef, Germany (1993); Utrecht, The Neth- lands (1994); Corfu, Greece (1995); Barcelona, Spain (1996); Graz, Austria (1997); Venice, Italy (1998); Prague, Czech Republic (1999); Saarbruc ¨ ken, Ger- ? many (2000), and Arhus, Denmark (2001). The predecessor to the Engineering and functions song of ESA used to be the once a year Workshop on set of rules En- neering (WAE). prior WAEs have been held in Venice, Italy (1997), Saarbruc ¨ ken, ? Germany (1998), London, united kingdom (1999), Saarbru ¨cken, Germany (2000), and Arhus, Denmark (2001). The court cases of the former ESAs have been released as Springer LNCS volumes 726, 855, 979, 1284, 1461, 1643, 1879, and 2161. The complaints of WAEs from 1999 onwards have been released as Springer LNCS volumes 1668, 1982, and 2161.

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Near-Linear Time Approximation Algorithms for Curve Simplification 37 Table 1. Comparing the size of simplifications produced by FrechetSimp with the optimal algorithm Curve 1 Curve 2 Size: 327 1998 ε Aprx. Exact Aprx. 2 Curve 3 9777 Aprx. Exact 6786 6431 4277 3197 1537 651 178 168 140 132 115 88 Experiments We now present experiments comparing our O(n log n) algorithm FrechetSimp with (i) the optimal O(n3 ) time Fr´echet simplification algorithm for quality; and (ii) with the Douglas-Peucker algorithm under Hausdorff error measure (with L2 metric) to demonstrate its efficiency.

We present experimental results demonstrating that our algorithms are simple and fast, and produce close to optimal simplifications in practice. 1 Introduction Given a polygonal curve, the curve simplification problem is to compute another polygonal curve that approximates the original curve, according to some predefined error criterion, and whose complexity is as small as possible. Curve simplification has useful applications in various fields, including geographic information systems (GIS), computer vision, graphics, image processing, and data compression.

Urrutia, editors, Handbook of Computational Geometry, pages 725–764. V. North-Holland, Amsterdam, 2000. 17 [17] M. Overmars. Efficient data structures for range searching on a grid. Journal of Algorithms, 9:254–275, 1988. 21, 22 [18] P. van Emde Boas. Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters, 6:80–82, 1977. 23 Near-Linear Time Approximation Algorithms for Curve Simplification Pankaj K. Agarwal1 , Sariel Har-Peled2 , Nabil H. edu Abstract.

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