By Euler L.

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We brieﬂy summarize the main contributions of our approach: We develop a general framework for retrieval of multimedia documents by example. , music, audio, image, and (relational) object retrieval). We propose generic algorithms for query evaluation together with eﬃcient algorithms for fault-tolerant retrieval which consequently exploit the structure inherent in the retrieval problems. In contrast to previously reported approaches, query evaluation becomes more eﬃcient when the complexity of a query increases.

Lasenby, Editors, Applications of Geometric Algebra in Computer Science and Engineering, Birkh¨ auser, Boston 2002. T. , New York, 1969. [7] T. L. White, Invariant Methods in Discrete and Computational Geometry: 245–256, Kluwer 1995. [8] D. Hestenes and G. Sobczyk, Cliﬀord Algebra to Geometric Calculus: A Uniﬁed Language for Mathematics and Physics, D. Reidel, Dordrecht, 1984, 1987. [9] D. Hestenes, and R. Ziegler (1991), Projective geometry with Cliﬀord algebra, Acta Applicandae Mathematicae, 23: 25–63.

As all stabilizers are trivial, each m ∈ M has a unique decomposition m = gm rm with gm ∈ G and rm ∈ R. Thus each m ∈ Di contributes exactly one entry to exactly one list: (gm , i) ∈ GD (rm ). • If m ∈ Di has a nontrivial stabilizer Gm and if m = gm r with gm ∈ G and r ∈ R, then m contributes exactly |Gm | entries to the inverted list GD (m), namely all pairs of the form (gm g, i) with g ∈ Gr . So if all stabilizers are small (|Gm | ≤ c, say) then a slight modiﬁcation of the above reasoning shows that the above equality can be replaced by r∈R length(GD (r)) ≤ c· i∈[1:N ] |Di |.