Competitive Capacitated Online Recoloring
Rajmohan Rajaraman, Omer Wasim

TL;DR
This paper introduces new competitive algorithms for online graph recoloring problems, achieving near-optimal bounds for various graph classes and dynamic settings with resource augmentation.
Contribution
It presents the first competitive algorithms for capacitated online recoloring and fully dynamic recoloring, with optimal or near-optimal bounds under resource augmentation.
Findings
Deterministic $O(rac{ ext{log} n}{ ext{resource augmentation}})$-competitive algorithm for bipartite graphs.
$O(n ext{log} n)$-competitive algorithm for fully dynamic recoloring.
Randomized $O(1)$-competitive algorithm for $ ext{max degree} = O( ext{sqrt}(n/ ext{log} n))$.
Abstract
In this paper, we revisit the online recoloring problem introduced recently by Azar et al. In online recoloring, there is a fixed set of vertices and an initial coloring for some . Under an online sequence of requests where each request is an edge , a proper vertex coloring of the graph induced by requests until time needs to be maintained for all ; i.e., for any , . The objective is to minimize the total weight of vertices recolored for the sequence . We obtain the first competitive algorithms for capacitated online recoloring and fully dynamic recoloring. Our first set of results is for -recoloring using algorithms that are -resource augmented where is an arbitrarily small constant. Our main result is an $O(\log…
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