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Robust Algorithms Under Adversarial Injections

Authors Paritosh Garg, Sagar Kale, Lars Rohwedder, Ola Svensson



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Author Details

Paritosh Garg
  • EPFL, Lausanne, Switzerland
Sagar Kale
  • University of Vienna, Austria
Lars Rohwedder
  • EPFL, Lausanne, Switzerland
Ola Svensson
  • EPFL, Lausanne, Switzerland

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Paritosh Garg, Sagar Kale, Lars Rohwedder, and Ola Svensson. Robust Algorithms Under Adversarial Injections. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 56:1-56:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.ICALP.2020.56

Abstract

In this paper, we study streaming and online algorithms in the context of randomness in the input. For several problems, a random order of the input sequence - as opposed to the worst-case order - appears to be a necessary evil in order to prove satisfying guarantees. However, algorithmic techniques that work under this assumption tend to be vulnerable to even small changes in the distribution. For this reason, we propose a new adversarial injections model, in which the input is ordered randomly, but an adversary may inject misleading elements at arbitrary positions. We believe that studying algorithms under this much weaker assumption can lead to new insights and, in particular, more robust algorithms. We investigate two classical combinatorial-optimization problems in this model: Maximum matching and cardinality constrained monotone submodular function maximization. Our main technical contribution is a novel streaming algorithm for the latter that computes a 0.55-approximation. While the algorithm itself is clean and simple, an involved analysis shows that it emulates a subdivision of the input stream which can be used to greatly limit the power of the adversary.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Theory of computation → Adversary models
Keywords
  • Streaming algorithm
  • adversary
  • submodular maximization
  • matching

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