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International Workshop on Algorithms and Computation

WALCOM 2017: WALCOM: Algorithms and Computation pp 335–346Cite as

Algorithms for Automatic Ranking of Participants and Tasks in an Anonymized Contest

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10167))

Abstract

We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task pair, we know whether the participant has succeeded at the task or not. We assume that participants vary in their ability to solve tasks, and that tasks vary in their difficulty to be solved. In an ideal world, stronger participants should succeed at a superset of tasks that weaker participants succeed at. Similarly, easier tasks should be completed successfully by a superset of participants who succeed at harder tasks. In reality, it can happen that a stronger participant fails at a task that a weaker participants succeeds at. Our goal is to find a perfect nesting of the participant-task relations by flipping a minimum number of participant-task relations, implying such a “nearest perfect ordering” to be the one that is closest to the truth of participant strengths and task difficulties. Many variants of the problem are known to be NP-hard.

We propose six natural k-near versions of the Chain Editing problem and classify their complexity. The input to a k-near Chain Editing problem includes an initial ordering of the participants (or tasks) that we are required to respect by moving each participant (or task) at most k positions from the initial ordering. We obtain surprising results on the complexity of the six k-near problems: Five of the problems are polynomial-time solvable using dynamic programming, but one of them is NP-hard.

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Acknowledgments

This work was supported in part by the US National Science Foundation under award numbers CCF-1527032, CCF-1655442, and IIS-1553547.

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Authors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania, 15213, USA

    Yang Jiao, R. Ravi & Wolfgang Gatterbauer

Authors
  1. Yang Jiao
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  2. R. Ravi
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  3. Wolfgang Gatterbauer
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Corresponding author

Correspondence to Yang Jiao .

Editor information

Editors and Affiliations

  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Jiao, Y., Ravi, R., Gatterbauer, W. (2017). Algorithms for Automatic Ranking of Participants and Tasks in an Anonymized Contest. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_26

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53924-9

  • Online ISBN: 978-3-319-53925-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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