TL;DR
This paper investigates the limits and possibilities of adversarially robust streaming algorithms for graph vertex coloring, establishing fundamental lower bounds and providing new algorithms with sublinear space complexity.
Contribution
It proves lower bounds on space and color usage for robust algorithms and introduces new algorithms that achieve colorings with sublinear space in adversarial streaming settings.
Findings
Robust $( ext{Delta}+1)$-coloring requires nearly $ ext{Omega}( ext{Delta}^2)$ colors
Robust $O( ext{Delta})$-coloring needs linear space $ ext{Omega}(n ext{Delta})$
New algorithms maintain $O( ext{Delta}^2)$- and $O( ext{Delta}^3)$-colorings with sublinear space
Abstract
A streaming algorithm is considered to be adversarially robust if it provides correct outputs with high probability even when the stream updates are chosen by an adversary who may observe and react to the past outputs of the algorithm. We grow the burgeoning body of work on such algorithms in a new direction by studying robust algorithms for the problem of maintaining a valid vertex coloring of an -vertex graph given as a stream of edges. Following standard practice, we focus on graphs with maximum degree at most and aim for colorings using a small number of colors. A recent breakthrough (Assadi, Chen, and Khanna; SODA~2019) shows that in the standard, non-robust, streaming setting, -colorings can be obtained while using only space. Here, we prove that an adversarially robust algorithm running under a similar space bound must…
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Videos
Adversarially Robust Coloring for Graph Streams· youtube
