# Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data

@inproceedings{Vial2018QuadraticTA, title={Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data}, author={Juan Jos{\'e} Besa Vial and William E. Devanny and David Eppstein and Michael T. Goodrich and Timothy Johnson}, booktitle={ALENEX}, year={2018} }

We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an adversary randomly swaps the order of adjacent items in the true sorted order. Previous work studies only two versions of quicksort, and has a gap between the lower bound of Omega(n) and the best upper bound of O(n log log n). The experiments we perform in this paper…

## 4 Citations

Optimally Sorting Evolving Data

- Computer ScienceICALP
- 2018

It is shown that a simple repeated insertion-sort algorithm can maintain an O(n) Kendall tau distance, with high probability, between a maintained list and an underlying total order of n items in an evolving data model where each comparison is followed by a swap between a random consecutive pair of items in the underlyingtotal order.

A Dynamic Model + BFR Algorithm for Streaming Data Sorting

- Computer ScienceIScIDE
- 2019

This work proposes a dynamic algorithm that can make full use of memory and minimize error to solve the problem of streaming data sorting, which is further combined with the BFR algorithm to sort a particular type of streamingData.

An Effective Approach to Analyze Algorithms with Linear O(n) Worst-Case Asymptotic Complexity

- Computer ScienceInternational Journal of Advanced Computer Science and Applications
- 2019

This paper provides an effective approach to analyze the algorithms belonging to the same class of asymptotes as the tables and graphs validates the results of the derived formula.

Interactive Learning of a Dynamic Structure

- Computer ScienceALT
- 2020

A general framework for interactively learning combinatorial structures, such as (binary or non-binary) classifiers, orderings/rankings of items, or clusterings, when the underlying structure changes over time is proposed, based on a graph representation of the structures and feedback in a static environment.

## References

SHOWING 1-10 OF 14 REFERENCES

Sorting and selection on dynamic data

- Computer ScienceTheor. Comput. Sci.
- 2011

Partial Sorting Problem on Evolving Data

- Computer ScienceAlgorithmica
- 2017

It is shown that the top-k-set problem, which means finding the top k elements without sorting them, can be solved error-free with probability 1-o(1) for all, and some extensions of the dynamic data model are considered that most of these results still hold.

PageRank on an evolving graph

- Computer Science, MathematicsKDD
- 2012

Under a stylized model of graph evolution, an algorithm is proposed that achieves a provable performance guarantee that is significantly better than the naive algorithm that crawls the nodes in a round-robin fashion.

Stable Matching with Evolving Preferences

- Computer ScienceAPPROX-RANDOM
- 2016

This work designs an algorithm that in expectation and with high probability maintains a matching that has at most $O((log (n)^2)$ blocking pairs.

Shortest Paths on Evolving Graphs

- Computer ScienceCSoNet
- 2016

A heuristic algorithm is proposed that takes into account time-dependent edge reliability and reduces the problem to find an edge-weighted shortest path and leads to higher precision and recall than those of the existing method.

Parameter Estimation in Large Dynamic Paired Comparison Experiments

- Mathematics
- 1999

Paired comparison data in which the abilities or merits of the objects being compared may be changing over time can be modelled as a non‐linear state space model. When the population of objects being…

Algorithms on evolving graphs

- Computer ScienceITCS '12
- 2012

A new general framework for computing with graphs that are evolving and massive in nature is defined, which captures the inherent tradeoff between the complexity of maintaining an up-to-date view of the graph and the quality of results computed with the available view.

Algorithm Design and Applications

- Computer Science
- 2014

Algorithm Design and Applications, by Michael T. Goodrich & Roberto Tamassia teaches students about designing and using algorithms, illustrating connections between topics being taught and their potential applications, increasing engagement.

A NEW MEASURE OF RANK CORRELATION

- Mathematics
- 1938

1. In psychological work the problem of comparing two different rankings of the same set of individuals may be divided into two types. In the first type the individuals have a given order A which is…