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For any forest $G = (V, E)$ it is possible to orient the edges $E$ so that no vertex in $V$ has out-degree greater than $1$. This paper considers the incremental edge-orientation problem, in which the edges $E$ arrive over time and the algorithm must maintain a low-out-degree edge orientation at all times. We give an algorithm that maintains a maximum out-degree of $3$ while flipping at most $O(log log n)$ edge orientations per edge insertion, with high probability in $n$. The algorithm requires worst-case time $O(log n log log n)$ per insertion, and takes amortized time $O(1)$. The previous state of the art required up to $O(log n / log log n)$ edge flips per insertion. We then apply our edge-orientation results to the problem of dynamic Cuckoo hashing. The problem of designing simple families $mathcal{H}$ of hash functions that are compatible with Cuckoo hashing has received extensive attention. These families $mathcal{H}$ are known to satisfy emph{static guarantees}, but do not come typically with emph{dynamic guarantees} for the running time of inserts and deletes. We show how to transform static guarantees (for $1$-associativity) into near-state-of-the-art dynamic guarantees (for $O(1)$-associativity) in a black-box fashion. Rather than relying on the family $mathcal{H}$ to supply randomness, as in past work, we instead rely on randomness within our table-maintenance algorithm.
In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk, least-element
Data is continuously generated by modern data sources, and a recent challenge in machine learning has been to develop techniques that perform well in an incremental (streaming) setting. In this paper, we investigate the problem of private machine lea
We present online algorithms for directed spanners and Steiner forests. These problems fall under the unifying framework of online covering linear programming formulations, developed by Buchbinder and Naor (MOR, 34, 2009), based on primal-dual techni
Motivated by the classic Generalized Assignment Problem, we consider the Graph Balancing problem in the presence of orientation costs: given an undirected multi-graph G = (V,E) equipped with edge weights and orientation costs on the edges, the goal i
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time periods wi