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Euro-Par 2013: Parallel Processing Workshops: BigDataCloud, DIHC, FedICI, HeteroPar, HiBB, LSDVE, MHPC, OMHI, PADABS, PROPER, Resilience, ROME, and UCHPC 2013, Aachen, Germany, August 26-27, 2013. Revised Selected Papers

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A function ft : V —► {0, l } m is an orderpreserving function if the lexicographic order over {0, l } m satisfies the relation ft(vi) >M«2) if vi >v2. (52) A function ft is a range-order-preserving function if ft is defined as a concatenation of two hash functions; h(v) = hi(v) o ft2(v), fti:F^{0,l}fc, (53) ft2: V ^ { 0 , l } m " * , and if fti is an order-preserving function. In general, it is difficult to design an order-preserving hash function for an arbitrary domain V. However, it is easy to design a range-order-preserving hash function for an arbitrary domain V.

10 3L5 5L13 ( , 0 R D # 4 ( , 0 R D # 7 | )) 3Q3 4TU 7L47 7Q43 8T37 7C139 A K-D-B tree organization of the relation in Fig. 9. 6" moves to the parent node, and causes its overflow. We use this delimiter again for the splitting of this overflowing node. This raises this delimiter "ORD# 6" to the root node. We show the result in Fig. 11. Unlike an extended fc-d tree [3], a fc-d trie [11], and a colored binary trie [13], a K-D-B tree has all its leaves at the bottom level, and hence has a constant directory search time for any kind of record values.

When we have N segments and n index attributes for which we want to minimize the access cost of equiselection queries, our colored-binary-trie segmentation scheme make the average access cost of equiselections on one attribute no more than O ^ " - 1 ) / " ) . This upper bound is proved to be of the same order as the theoretical lower bound of the average access cost nedessary for equiselections on an arbitrary attribute out of n index attributes. This cost reaches O(N) as n becomes large. Therefore, for large n, any multiattribute segmentation scheme becomes meaningless.

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