Preprocessing Ambiguous Imprecise Points

Hoog, Ivor van der; Kostitsyna, Irina; Löffler, Maarten; Speckmann, Bettina

doi:10.4230/lipics.socg.2019.42

Cited by 3 publications

(3 citation statements)

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“…Halldórsson and de Lima [22] presented better query-competitive algorithms, by using randomization or assumptions on the underlying graph structure. Other related work on sorting has considered sorting with noisy information [1,6] or preprocessing the uncertain intervals so that the actual numbers can be sorted efficiently once their precise values are revealed [33].…”

Section: Introductionmentioning

confidence: 99%

Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Erlebach

Hoffmann

Lima³

2022

Algorithmica

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In computing with explorable uncertainty, one considers problems where the values of some input elements are uncertain, typically represented as intervals, but can be obtained using queries. Previous work has considered query minimization in the settings where queries are asked sequentially (adaptive model) or all at once (non-adaptive model). We introduce a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. Using competitive analysis, we present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds for the given instance. Given a set of uncertain elements and a family of m subsets of that set, we study the problems of sorting all m subsets and of determining the minimum value (or the minimum element(s)) of each subset. We also study the selection problem, i.e., the problem of determining the i-th smallest value and identifying all elements with that value in a given set of uncertain elements. Our results include 2-round-competitive algorithms for sorting and selection and an algorithm for the minimum value problem that uses at most $$(2+\varepsilon ) \cdot \mathrm {opt}_k+\mathrm {O}\left( \frac{1}{\varepsilon } \cdot \lg m\right) $$ ( 2 + ε ) · opt k + O 1 ε · lg m query rounds for every $$0<\varepsilon <1$$ 0 < ε < 1 , where $$\mathrm {opt}_k$$ opt k is the optimal number of query rounds.

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Section: Introductionmentioning

confidence: 99%

Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Erlebach

Hoffmann

Lima³

2022

Algorithmica

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“…Halldórsson and de Lima [21] presented better query-competitive algorithms, by using randomization or assumptions on the underlying graph structure. Other related work on sorting has considered sorting with noisy information [1,6] or preprocessing the uncertain intervals so that the actual numbers can be sorted efficiently once their precise value are revealed [31].…”

Section: Introductionmentioning

confidence: 99%

Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Erlebach¹,

Hoffmann²,

Lima³

2021

Preprint

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The area of computing with uncertainty considers problems where some information about the input elements is uncertain, but can be obtained using queries. For example, instead of the weight of an element, we may be given an interval that is guaranteed to contain the weight, and a query can be performed to reveal the weight. While previous work has considered models where queries are asked either sequentially (adaptive model) or all at once (non-adaptive model), and the goal is to minimize the number of queries that are needed to solve the given problem, we propose and study a new model where k queries can be made in parallel in each round, and the goal is to minimize the number of query rounds. We use competitive analysis and present upper and lower bounds on the number of query rounds required by any algorithm in comparison with the optimal number of query rounds. Given a set of uncertain elements and a family of m subsets of that set, we present an algorithm for determining the value of the minimum of each of the subsets that requires at most, where opt k is the optimal number of rounds, as well as nearly matching lower bounds. For the problem of determining the i-th smallest value and identifying all elements with that value in a set of uncertain elements, we give a 2-round-competitive algorithm. We also show that the problem of sorting a family of sets of uncertain elements admits a 2-round-competitive algorithm and this is the best possible. ACM Subject ClassificationTheory of Computation → Design and analysis of algorithms; Mathematics of computing → Discrete mathematics; Theory of computation → Theory and algorithms for application domains

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“…Other related work. One interesting related problem was studied by van der Hoog et al [29]: how to preprocess a set of intervals so that the the actual numbers can be sorted efficiently after their precise values are revealed. Ajtai et al [2] studied an uncertainty variant of the sorting problem in which a comparison between two values may be imprecise, and the goal is to minimize the number of comparisons to sort the values within a given precision.…”

Section: Introductionmentioning

confidence: 99%

Query Minimization under Stochastic Uncertainty

Chaplick,

Halldórsson,

de Lima

et al. 2020

Preprint

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We study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration while minimizing the expected total query cost. We show that sorting in this scenario can be performed in polynomial time. For the problem of finding the data item with minimum value, we have some evidence for hardness. This contradicts intuition, since the minimum problem is easier both in the online setting with adversarial inputs and in the offline verification setting. However, the stochastic assumption can be leveraged to beat both deterministic and randomized approximation lower bounds for the online setting.

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Preprocessing Ambiguous Imprecise Points

Cited by 3 publications

References 0 publications

Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Round-Competitive Algorithms for Uncertainty Problems with Parallel Queries

Query Minimization under Stochastic Uncertainty

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