Theory and Implementation of Online Multiselection Algorithms

Barbay, Jérémy; Gupta, Ankur; Jo, Seungbum; Satti, Srinivasa Rao; Sorenson, Jonathan

doi:10.1007/978-3-642-40450-4_10

Cited by 4 publications

(4 citation statements)

References 12 publications

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“…At first view, one could hope to generalized the refined entropy analysis (introduced by Kaligosi et al [14] and applied by Barbay et al [1] to the online version) of MULTISETS deferred data structures supporting rank and select to the computational complexity of optimal prefix free codes: a complexity proportional to the entropy of the distribution of codelengths in the output would nicely match the lower bound of Ω(k (1 + H(n 1 , . . .…”

Section: Applicability Of Refined Results On Deferred Data Structuresmentioning

confidence: 99%

“…Karp et al's analysis [15] of the complexity of the deferred data structure is in function of the total number q of queries and operators, while Kaligosi et al [14] analyzed the complexity of an offline version in function of the size of the gaps between the positions of the queries. Barbay et al [1] combined the three results into a single deferred data structure for MULTISETS which supports the operators rank and select in amortized time proportional to the entropy of the distribution of the sizes of the gaps between the positions of the queries.…”

Section: Applicability Of Refined Results On Deferred Data Structuresmentioning

confidence: 99%

“…When answering a partialSum query, perform a select query and then return the value of the partial sum corresponding to the value by the select query: the asymptotic complexity is within a constant factor of the one described by Karp et al [15]. ⊓ ⊔ Barbay et al [1] further improved Karp et al's result [15] with a simpler data structure (a single binary array) and a finer analysis taking into account the gaps between the position hit by the queries. Barbay et al's results [1] can similarly be augmented in order to support partialSum queries while increasing the computational complexity by only a constant factor.…”

Section: Partial Sum Deferred Data Structurementioning

confidence: 99%

“…⊓ ⊔ Barbay et al [1] further improved Karp et al's result [15] with a simpler data structure (a single binary array) and a finer analysis taking into account the gaps between the position hit by the queries. Barbay et al's results [1] can similarly be augmented in order to support partialSum queries while increasing the computational complexity by only a constant factor. This result is not relevant to the analysis described in Section 3.…”

Section: Partial Sum Deferred Data Structurementioning

confidence: 99%

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Optimal Prefix Free Codes with Partial Sorting

Barbay

2019

Algorithms

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We describe an algorithm computing an optimal prefix free code for n unsorted positive weights in time within O(n(1 + lg α)) ⊆ O(n lg n), where the alternation α ∈ [1..n − 1] measures the amount of sorting required by the computation. This asymptotical complexity is within a constant factor of the optimal in the algebraic decision tree computational model, in the worst case over all instances of size n and alternation α. Such results refine the state of the art complexity of Θ(n lg n) in the worst case over instances of size n in the same computational model, a landmark in compression and coding since 1952, by the mere combination of van Leeuwen's algorithm to compute optimal prefix free codes from sorted weights (known since 1976), with Deferred Data Structures to partially sort a multiset depending on the queries on it (known since 1988).

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Section: Applicability Of Refined Results On Deferred Data Structuresmentioning

confidence: 99%

Section: Applicability Of Refined Results On Deferred Data Structuresmentioning

confidence: 99%

Section: Partial Sum Deferred Data Structurementioning

confidence: 99%

Section: Partial Sum Deferred Data Structurementioning

confidence: 99%

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Optimal Prefix Free Codes with Partial Sorting

Barbay

2019

Algorithms

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Dynamic Online Multiselection in Internal and External Memory

Barbay

Gupta

Satti

et al. 2015

WALCOM: Algorithms and Computation

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Near-optimal online multiselection in internal and external memory

Barbay

Gupta

Satti

et al. 2016

Journal of Discrete Algorithms

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We introduce an online version of the multiselection problem, in which q selection queries are requested on an unsorted array of nelements. We provide the first online algorithm that is 1-competitive with the offline algorithm proposed by Kaligosi et al. [14] in terms of comparison complexity. Our algorithm also supports online searchqueries efficiently. We then extend our algorithm to the dynamic setting, while retaining online functionality, by supporting arbitrary insertions and deletions on the array. Assuming that the insertion of an element is immediately preceded by a search for that element, our dynamic online algorithm performs an optimal number of comparisons, up to lower order terms and an additive O(n) term. For the external memory model, we describe the first online multiselection algorithm that is O(1)-competitive. This result improves upon the work of Sibeyn [20] when q = omega(m(1-epsilon)) for any fixed positive constant epsilon, where m is the number of blocks that can be stored in main memory. We also extend it to support searches, insertions, and deletions of elements efficiently

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Theory and Implementation of Online Multiselection Algorithms

Cited by 4 publications

References 12 publications

Optimal Prefix Free Codes with Partial Sorting

Optimal Prefix Free Codes with Partial Sorting

Dynamic Online Multiselection in Internal and External Memory

Near-optimal online multiselection in internal and external memory

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