Separating sublinear time computations by approximate diameter

We study the problem of separating sublinear time computations via approximating the diameter for a sequence S = p 1 p 2 ⋅⋅⋅ p n of points in a metric space, in which any two consecutive points have the same distance. The computation is considered respectively under deterministic, zero error randomi...

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Veröffentlicht in:Journal of combinatorial optimization Jg. 18; H. 4; S. 393 - 416
Hauptverfasser: Fu, Bin, Zhao, Zhiyu
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.11.2009
Springer
Schlagworte:
Applied sciences
Combinatorics
Convex and Discrete Geometry
Exact sciences and technology
Flows in networks. Combinatorial problems
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Theory of Computation
Randomization
Separation of complexity classes
Sublinear time algorithm
Diameter
Complexity class
Metric space
Query
Error bound
Randomized algorithm
Combinatorial optimization
Modeling
Computation time
Randomized design
ISSN:1382-6905, 1573-2886
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Zusammenfassung:We study the problem of separating sublinear time computations via approximating the diameter for a sequence S = p 1 p 2 ⋅⋅⋅ p n of points in a metric space, in which any two consecutive points have the same distance. The computation is considered respectively under deterministic, zero error randomized, and bounded error randomized models. We obtain a class of separations using various versions of the approximate diameter problem based on restrictions on input data. We derive tight sublinear time separations for each of the three computation models via proving that computation with O ( n r ) time is strictly more powerful than that with O ( n r − ε ) time, where r and ε are arbitrary parameters in (0,1) and (0, r ) respectively. We show that, for any parameter r ∈(0,1), the bounded error randomized sublinear time computation in time O ( n r ) cannot be simulated by any zero error randomized sublinear time algorithm in o ( n ) time or queries; and the same is true for zero error randomized computation versus deterministic computation.
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-009-9248-3