@inproceedings{c9feadcc7a7648c19b6a27c2a3b068b6,

title = "Geometric pattern matching in d-dimensional space",

abstract = "We show that, using the L∞ metric, the minimum Hausdorff distance under translation between two point sets of cardinality n in ddimensional space can be computed in time O(n(4d-2)/31og2 n) for d > 3. Thus we improve the previous time bound of O(n2d-2 log2 n) due to Chew and Kedem. For d = 3 we obtain a better result of O(n3 log2 n) time by exploiting the fact that the union of n axis-parallel unit cubes can be decomposed into O(n) disjoint axls-parallel boxes. We prove that the number of different translations that azhieve the minimum Hausdorff distance in dspace is Θ (n[3d/2]). Furthermore, we present an algorithm which computes the minimum Hausdorff distance under the L2 metric in d-space in time O(n[3d/2]+l log3 n).",

author = "Chew, {L. Paul} and Dorit Dor and Alon Efrat and Klara Kedem",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1995.; 3rd Annual European Symposium on Algorithms, ESA 1995 ; Conference date: 25-09-1995 Through 27-09-1995",

year = "1995",

month = jan,

day = "1",

language = "English",

isbn = "3540603131",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "264--279",

editor = "Paul Spirakis",

booktitle = "Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings",

address = "Germany",

}