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Introduction Many widely used file organizations can be logically partitioned into two components; the index (also called directory) component and the data leaves component. The file records are maintained in data leaves where each data leaf (leaf for short) is one logical unit which is stored in contiguous disk pages. The index component is a search structure, usually a tree or a hash table, which is used, given a key of a desired record, to search for the appropriate data leaf. Examples of such single-key file organizations are B+-trees and its variants [4], and the Extendible Hash method [6], and examples of such multi-attribute (i.e. multi-key) file organizations are the Grid File [10], the k-d tree [2;, and the hB-tree [9]. When using these organizations, an effort is made to store the entire index in main memory in order to decrease the operations execution cost and by that to improve performance. However, as main memory 1S a valuable resource, this is usually not possible. This motivates the desire to decrease the index size, so that it can fit into main memory. An efficient method for decreasing the index size, and which is applicable to each of the above mentioned organizations, is the use of multi-bucket leaves. A multi-bucket leaf consists of L > 1 primary buckets and one overflow bucket. When a record need be inserted to a multi-bucket leaf, the primary bucket into which it is inserted is chosen by using a hash function. If the chosen primary bucket is full then the record is inserted to the overflow bucket. If the overflow bucket is full as well, then the multi-bucket leaf is split i.e. it is replaced with two multi-bucket leaves and its records are partitioned between these two leaves according to some chosen split key. A multi-bucket leaf is stored in contiguous disk pages (Le. its buckets are stored contiguously), and in order to perform a single-key operation (search, update, insert, or delete) only the appropriate primary bucket is read and if required, the overflow bucket is read as well. Due to an anomalous behavior of the hash function, some of the primary buckets of a. multi­ bucket leaf may be overloaded while other primary buckets of the same multi-bucket leaf are not loaded. Following a split of this multi-bucket leaf, such an anomalous situation may continue to hold in the two leaves that replace the split …