Mixing time for the Repeated Balls into Bins dynamics
نویسندگان
چکیده
منابع مشابه
Balls into Bins Made Faster
Balls-into-bins games describe in an abstract setting several multiple-choice scenarios, and allow for a systematic and unified theoretical treatment. In the process that we consider, there are n bins, initially empty, and m = bcnc balls. Each ball chooses independently and uniformly at random k ≥ 3 bins. We are looking for an allocation such that each ball is placed into one of its chosen bins...
متن کاملBalanced Allocations: Balls-into-Bins Revisited and Chains-into-Bins
The study of balls-into-bins games or occupancy problems has a long history since these processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins game is to allocate a set of independent objects (tasks, jobs, balls) to a set of resources (servers, bins, urns) and, thereby, to minimize the maximum load. In this paper ...
متن کاملOn Weighted Balls-into-Bins Games
We consider the well-known problem of randomly allocating m balls into n bins. We investigate various properties of single-choice games as well as multiple-choice games in the context of weighted balls. We are particularly interested in questions that are concerned with the distribution of ball weights, and the order in which balls are allocated. Do any of these parameters influence the maximum...
متن کاملBalls into Bins via Local Search
We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. In our main result, we prove that this process yields a maximum ...
متن کاملThe (1 + β)-Choice Process and Weighted Balls-into-Bins
Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well-known that the gap between the load of the most loaded bin and the average is Θ( √ m logn n ), for large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to Θ(log logn) independent of m. Consider now the following “(1 + β)-choice” process for some par...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2020
ISSN: 1083-589X
DOI: 10.1214/20-ecp338