Distribution-sensitive set multi-partitioning

Given a set $\mathcal{S}$ with real-valued members, associated with each member one of two possible types; a multi-partitioning of $\mathcal{S}$ is a sequence of the members of $\mathcal{S}$ such that if $x,y \in \mathcal{S}$ have different types and $x < y$, $x$ precedes $y$ in the multi-partiti...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings vol. AD,...; no. Proceedings; pp. 353 - 356
Main Author: Elmasry, Amr
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 01.01.2005
Discrete Mathematics and Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science
Series:DMTCS Proceedings
Subjects:
[info.info-cg] computer science [cs]/computational geometry [cs.cg]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
[math.math-co] mathematics [math]/combinatorics [math.co]
algorithm analysis and design
Combinatorics
Computational Geometry
Computer Science
Data Structures and Algorithms
Discrete Mathematics
distribution-sensitive algorithms
lower bounds
Mathematics
output-sensitive algorithms
output-sensitive algorithms
algorithm analysis and design
distribution-sensitive algorithms
lower bounds
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:Given a set $\mathcal{S}$ with real-valued members, associated with each member one of two possible types; a multi-partitioning of $\mathcal{S}$ is a sequence of the members of $\mathcal{S}$ such that if $x,y \in \mathcal{S}$ have different types and $x < y$, $x$ precedes $y$ in the multi-partitioning of $\mathcal{S}$. We give two distribution-sensitive algorithms for the set multi-partitioning problem and a matching lower bound in the algebraic decision-tree model. One of the two algorithms can be made stable and can be implemented in place. We also give an output-sensitive algorithm for the problem.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.3381