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The Tree-Encoded Bitmap (TEB) is a tree-based bitmap compression scheme that maps runs in a bitmap to leaf nodes in a binary tree.Currently, TEBs perform updates using an auxiliary differential data structure. However, consulting this additional data structure at every read introduces both memory and read overheads. To mitigate the shortcomings of differential updates, we propose algorithms to update TEBs in place. To that end, we classify the updates that can occur in a TEB into two types: run-forming and run-breaking.Run-forming updates correspond to leaf nodes at the lowest level of the binary tree. All other updates are run-breaking. Each type of update requires different handling. Through experimentation with synthetic data, we determined that in-place run-forming updates are 2-3× faster than differential updates, while run-breaking updates cannot be efficiently performed in place. Therefore, we propose a hybrid solution that performs run-forming updates in place and stores run-breaking updates in a differential data structure. Our experiments with synthetic data show that our hybrid solution performs updates faster than the differential approach. For example, for a workload where 20% of the updates are run forming, our hybrid solution is 69% faster on average.

Graphs in many applications, such as social networks and IoT, are inherently streaming, involving continuous additions and deletions of vertices and edges at high rates. Constructing random walks in a graph, i.e., sequences of vertices selected with a specific probability distribution, is a prominent task in many of these graph applications as well as machine learning (ML) on graph-structured data. In a streaming scenario, random walks need to constantly keep up with the graph updates to avoid stale walks and thus, performance degradation in the downstream tasks. We present Wharf, a system that efficiently stores and updates random walks on streaming graphs. It avoids a potential size explosion by maintaining a compressed, high-throughput, and low-latency data structure. It achieves (i) the succinct representation by coupling compressed purely functional binary trees and pairing functions for storing the walks, and (ii) efficient walk updates by effectively pruning the walk search space. We evaluate Wharf, with real and synthetic graphs, in terms of throughput and latency when updating random walks. The results show the high superiority of Wharf over inverted index- and tree-based baselines.

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