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dc.contributor.authorHoffmann, Michael-
dc.contributor.authorIacono, John-
dc.contributor.authorNicholson, Patrick K.-
dc.contributor.authorRaman, Rajeev-
dc.identifier.citationTheoretical Computer Science, 2017, in pressen
dc.descriptionThe file associated with this record is under embargo until 24 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.en
dc.description.abstractIn nearest larger value (NLV) problems, we are given an array A[1..n] of distinct numbers, and need to preprocess A to answer queries of the following form: given any index i∈[1,n], return a “nearest” index j such that A[j]>A[i]. We consider the variant where the values in A are distinct, and we wish to return an index j such that A[j]>A[i] and|j−i| is minimized, the nondirectional NLV (NNLV) problem. We consider NNLV in the encoding model, where the array A is deleted after preprocessing. The NNLV encoding problem turns out to have an unexpectedly rich structure: the effective entropy (optimal space usage) of the problem depends crucially on details in the definition of the problem. Of particular interest is the tiebreaking rule: if there exist two nearest indices j1,j2 such that A[j1]>A[i] and A[j2]>A[i] and |j1−i|=|j2−i|, then which index should be returned? For the tiebreaking rule where the rightmost (i.e., largest) index is returned, we encode a path-compressed representation of the Cartesian tree that can answer all NNLV queries in 1.89997n+o(n) bits, and can answer queries inO(1) time. An alternative approach, based on forbidden patterns , achieves a very similar space bound for two tiebreaking rules (including the one where ties are broken to the right), and (for a more flexible tiebreaking rule) achieves 1.81211n+o(n) bits. Finally, we develop a fast method of counting distinguishable configurations for NNLV queries. Using this method, we prove a lower bound of 1.62309n−Θ(1) bits of space for NNLV encodings for the tiebreaking rule where the rightmost index is returned.en
dc.rightsCopyright © 2017, Elsevier. Deposited with reference to the publisher’s open access archiving policy.en
dc.subjectData structuresen
dc.subjectEncoding data structuresen
dc.subjectSuccinct data structuresen
dc.titleEncoding Nearest Larger Valuesen
dc.typeJournal Articleen
pubs.organisational-group/Organisation/COLLEGE OF SCIENCE AND ENGINEERINGen
pubs.organisational-group/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Scienceen
Appears in Collections:Published Articles, Dept. of Computer Science

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