Online Mincut: Advice, Randomization and More
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In this paper we study the mincut problem on connected graphs in the online setting. We consider the vertex arrival model; whenever a new vertex arrives it's adjacency to previously revealed vertices are given. An online algorithm must make an irrevocable decision to determine the side of the cut that the vertex must belong to in order to minimize the size of the cut. Various models are considered. 1) For classical and advice models we give tight bounds on the competitive ratio of deterministic algorithms. 2) Next we consider few semi-adversarial inputs: random order of arrival with adversarially generated and sparse graphs. 3) Lastly we introduce a new model, which we call the friendly sequence model. We look at several online optimization problems : mincut, maxcut and submodular maximization and show that there are input ordering where a greedy strategy can produce an optimal answer.
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