Date of Award

Spring 2024

Document Type

Thesis (Ph.D.)

Department or Program

Computer Science

First Advisor

Amit Chakrabarti

Abstract

A streaming algorithm has a limited amount of memory and reads a long sequence (data stream) of input elements, one by one, and computes an output depending on the input. Such algorithms may be used in an online fashion, producing a sequence of intermediate outputs corresponding to the prefixes of the data stream. Adversarially robust streaming algorithms are required to give correct outputs with a desired probability even when the data stream is adaptively generated by an adversary that can see all intermediate outputs of the algorithm. This thesis binds together research on a variety of problems related to the adversarial setting and other models for streaming algorithms.

  • A toy problem in streaming called "Missing Item Finding" is studied in a variety of models, including: classical, adversarially robust, white-box adversarially robust, pseudo-deterministic, and deterministic streaming. Surprisingly, we find that for a wide range of problem parameters, adversarially robust algorithms for Missing Item Finding require access to a random oracle to work efficiently, requiring exponentially more space otherwise.
  • We find lower and upper bounds for adversarially robust algorithms using semi-streaming space, which solve the task of maintaining an O(Δc)-vertex-coloring of a graph edge insertion stream, for all constants c > 1. These give separations relative to classical and deterministic streaming. We also give a deterministic multi-pass algorithm for (Δ+1)-vertex-coloring.
  • We obtain streaming algorithms for online edge coloring of graph edge insertion and vertex insertion streams that use sublinear space in the O(Δ)-color regime; our algorithms can handle multi-graph streams, can be made deterministic, and give smooth space/color tradeoffs.

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