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Abstract Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus quickly retrieve all edges between two sets of nodes (anode-based slice) but cannot quickly retrieve all edges that occur within a given time interval (atime-based slice). We propose a hybrid data structure for storing temporal networks that stores edges in both an adjacency dictionary, enabling rapid node-based slices, and an interval tree, enabling rapid time-based slices. Our hybrid structure also enablescompound slices, where one needs to slice both over nodes and time, either by slicing first over nodes or slicing first over time. We further propose an approach for predictive compound slicing, which attempts to predict whether a node-based or time-based compound slice is more efficient. We evaluate our hybrid data structure on many real temporal network data sets and find that they achieve much faster slice times than existing data structures with only a modest increase in creation time and memory usage.
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Stability of polydisc slicing
Abstract We prove a dimension‐free stability result for polydisc slicing due to Oleszkiewicz and Pełczyński. Intriguingly, compared to the real case, there is an additional asymptotic maximizer. In addition to Fourier‐analytic bounds, we crucially rely on a self‐improving feature of polydisc slicing, established via probabilistic arguments.
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- Award ID(s):
- 2246484
- PAR ID:
- 10465626
- Publisher / Repository:
- Oxford University Press (OUP)
- Date Published:
- Journal Name:
- Mathematika
- Volume:
- 69
- Issue:
- 4
- ISSN:
- 0025-5793
- Format(s):
- Medium: X Size: p. 1165-1182
- Size(s):
- p. 1165-1182
- Sponsoring Org:
- National Science Foundation
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