Sorting and selection on dynamic data

Anagnostopoulos, Aris; Kumar, Raman; Mahdian, Mohammad; Upfal, Eli

doi:10.1016/j.tcs.2010.10.003

Cited by 9 publications

(53 citation statements)

References 1 publication

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“…At each time step t, the weights of the edges induce an ordering π t on the edge set E. The ordering π t+1 is obtained from π t by swapping a random consecutive pair. As argued in [2], this is perhaps the most natural model for gradual change with ordinal weights, and as we will see, an ordinal weighted model is rich enough to capture the evolving MST problem.…”

Section: Modelmentioning

confidence: 88%

“…We follow the general framework defined in [2] for algorithms on dynamic data. In the case of evolving graphs, this model can be described as follows.…”

Section: Modelmentioning

confidence: 99%

“…For weighted graphs, we assume an ordinal model of change similar to the one in [2]: the edge set is fixed (i.e., Et = E for all t), and only the weights change. At each time step t, the weights of the edges induce an ordering π t on the edge set E. The ordering π t+1 is obtained from π t by swapping a random consecutive pair.…”

Section: Modelmentioning

confidence: 99%

“…Our first algorithm is as follows: we use the simple sorting algorithm of [2] to keep an approximationπ t of the real ordering π t of all the O(n 2 ) edges. At each time step, our first algorithm returns the tree built using Kruskal's greedy algorithm onπ t (i.e., the MST for orderingπ t ).…”

Section: The Algorithm and Analysismentioning

confidence: 99%

“…To address some of the challenges of interest that are not captured by the aforementioned models, we propose a new computational framework on graphs where the underlying graph changes over time and an algorithm can only observe these changes by probing the graph in a limited way. This evolving graph framework is inspired by the work of Anagnostopoulos et al [2], who studied sorting and selection problems in an evolving (scalar) data setting. In our framework, the graph changes over time without notifying the algorithm and therefore the algorithm needs to periodically probe the graph to learn about new changes and update its solution accordingly.…”

Section: Introductionmentioning

confidence: 99%

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Algorithms on evolving graphs

Anagnostopoulos

Kumar

Mahdian

et al. 2012

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

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Motivated by applications that concern graphs that are evolving and massive in nature, we define a new general framework for computing with such graphs. In our framework, the graph changes over time and an algorithm can only track these changes by explicitly probing the graph. This framework 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. We apply this framework to two classical graph connectivity problems, namely, path connectivity and minimum spanning trees, and obtain efficient algorithms.

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Section: Modelmentioning

confidence: 88%

“…We follow the general framework defined in [2] for algorithms on dynamic data. In the case of evolving graphs, this model can be described as follows.…”

Section: Modelmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: The Algorithm and Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Algorithms on evolving graphs

Anagnostopoulos

Kumar

Mahdian

et al. 2012

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

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Generating Almost Descending Sequences to Reduce the Number of Movements in Sorting

Xiao

2022

IEEE Access

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Sorting algorithms usually generate strictly descending sequences. However, almost descending sequences may be sufficient to fulfill our needs in practice, and the number of movements needed for generating such sequences can be greatly reduced. We call a sequence S almost descending if S[j] − S[i] < C for any i < j and a positive number C, which depends on the practical circumstances. Unless the difference between S[j] and S[i] exceeds the bound C, we deem them indistinguishable. For example, when people are arranged in a line from tall to short, two people with heights of 1.751 meters and 1.752 meters can be considered visually indistinguishable (we can set the bound to C = 0.005 meters in this case). Therefore, we do not need to adjust their positions, which leads to fewer movements in sorting. In this paper, three algorithms are provided to generate almost descending sequences, and their correctness is proven. The experimental results of the proposed algorithms demonstrate that our technique can reduce the number of movements in sorting. In addition, almost descending sequences are more stable than strictly descending sequences in dynamic sorting, which is useful in online sorting and sorting in noisy environments.

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Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data

Vial¹,

Devanny

Eppstein

et al. 2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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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 Ω(n) and the best upper bound of O(n log log n). The experiments we perform in this paper provide empirical evidence that some quadratic-time algorithms such as insertion sort and bubble sort are asymptotically optimal for any constant rate of random swaps. In fact, these algorithms perform as well as or better than algorithms such as quicksort that are more efficient in the traditional algorithm analysis model.

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Sorting and selection on dynamic data

Cited by 9 publications

References 1 publication

Algorithms on evolving graphs

Algorithms on evolving graphs

Generating Almost Descending Sequences to Reduce the Number of Movements in Sorting

Quadratic Time Algorithms Appear to be Optimal for Sorting Evolving Data

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