Storing Partitions of Integers in Sublinear Space

Kentaro Sumigawa () and Kunihiko Sadakane ()
Additional contact information
Kentaro Sumigawa: The University of Tokyo
Kunihiko Sadakane: The University of Tokyo

The Review of Socionetwork Strategies, 2019, vol. 13, issue 2, 237-252

Abstract: Abstract In this study, we introduce a data structure representing a partition of an integer n, which uses $$\mathrm{O}(\sqrt{n})$$ O ( n ) bits of space. This is a constant multiple of the information theoretic lower bound. Three types of operations $${\textsf {access}}_{{\textsf {p}}}$$ access p , $${\textsf {bound}}_{{\textsf {p}}}$$ bound p , $${\textsf {prefixsum}}_{{\textsf {p}}}$$ prefixsum p 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 $$\mathrm{O}(\min \{\frac{1}{\delta }u \left( \frac{n}{u}\right) ^{\delta }, \frac{1}{\delta }n\left( \frac{u}{n}\right) ^\delta \})$$ O ( min { 1 δ u n u δ , 1 δ n u n δ } ) bits of space for any positive constant $$\delta $$ δ where n is the number of terms, and u denotes the size of the universe.

Keywords: Partition of integer; Monotonic sequence; Succinct data structure (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12626-019-00044-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:trosos:v:13:y:2019:i:2:d:10.1007_s12626-019-00044-2

Ordering information: This journal article can be ordered from
https://www.springer ... ystems/journal/12626

DOI: 10.1007/s12626-019-00044-2

Access Statistics for this article

The Review of Socionetwork Strategies is currently edited by Katsutoshi Yada, Yasuharu Ukai and Marshall Van Alstyne

More articles in The Review of Socionetwork Strategies from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().