Storing Partitions of Integers in Sublinear Space
The Review of Socionetwork Strategies(2019)
摘要
In this study, we introduce a data structure representing a partition of an integer n , which uses O(√(n)) bits of space. This is a constant multiple of the information theoretic lower bound. Three types of operations _ , _ , _ are supported in constant time using the notion of conjugate of a partition. To construct this data structure, we establish a data structure representing a monotonic sequence, which supports the same operations in constant time and uses O(min{1/δu ( n/u) ^δ, 1/δn( u/n) ^δ}) bits of space for any positive constant δ where n is the number of terms, and u denotes the size of the universe.
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关键词
Partition of integer,Monotonic sequence,Succinct data structure
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