An Efficient Noisy Binary Search in Graphs via Median Approximation

Dereniowski, Dariusz; Łukasiewicz, Aleksander; Uznański, Przemysław

doi:10.1007/978-3-030-79987-8_19

Cited by 4 publications

(3 citation statements)

References 36 publications

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“…This is due to the fact that the problem for paths is the classical binary search, where most of the focus has been on noisy comparison models, see e.g. [3,15,18,19,24,30]. As for the case of trees, they generalize binary search to searching partial orders with some interesting applications e.g.…”

Section: Related Workmentioning

confidence: 99%

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Edge and Pair Queries-Random Graphs and Complexity

Dereniowski

Gordinowicz

Prałat³

2023

Electron. J. Combin.

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Section: Related Workmentioning

confidence: 99%

“…On the other hand, there has been a series of results on approximation algorithms [13,14,16] with the best approximation ratio to date being O( √ log n) that was proved in [17]. Finally, let us mention another generalization of binary search in linear orders to graphs [23,19] with some interesting applications in machine learning [22].…”

Section: Related Workmentioning

confidence: 99%

Edge and Pair Queries-Random Graphs and Complexity

Dereniowski

Gordinowicz

Prałat³

2023

Electron. J. Combin.

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“…We generalize the idea for a tree with any structure that allows us to apply the method to a wide class of tree data structures. Different algorithms for noisy search, especially a noisy tree, and graph processing and search were considered in [2][3][4][5][6][7][8]. We apply our technique to two tree data structures.…”

Section: Introductionmentioning

confidence: 99%

Noisy Tree Data Structures and Quantum Applications

Khadiev,

Savelyev,

Ziatdinov

et al. 2023

Mathematics

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We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound.

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Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees

2022

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We study the problem of designing a resilient data structure maintaining a tree under the Faulty-RAM model [Finocchi and Italiano, STOC’04] in which up to $$\delta $$ δ memory words can be corrupted by an adversary. Our data structure stores a rooted dynamic tree that can be updated via the addition of new leaves, requires linear size, and supports resilient (weighted) level ancestor queries, lowest common ancestor queries, and bottleneck vertex queries in $$O(\delta )$$ O ( δ ) worst-case time per operation.

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An Efficient Noisy Binary Search in Graphs via Median Approximation

Cited by 4 publications

References 36 publications

Edge and Pair Queries-Random Graphs and Complexity

Edge and Pair Queries-Random Graphs and Complexity

Noisy Tree Data Structures and Quantum Applications

Resilient Level Ancestor, Bottleneck, and Lowest Common Ancestor Queries in Dynamic Trees

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