Deterministic and Low-Span Work-Efficient Parallel Batch-Dynamic Trees
Pages 247 - 258
Abstract
Dynamic trees are a well-studied and fundamental building block of dynamic graph algorithms dating back to the seminal work of Sleator and Tarjan [STOC'81, (1981), pp. 114-122]. The problem is to maintain a tree subject to online edge insertions and deletions while answering queries about the tree, such as the heaviest weight on a path, etc. In the parallel batch-dynamic setting, the goal is to process batches of edge updates work efficiently in low (polylog n) span. Two work-efficient algorithms are known: batch-parallel Euler Tour Trees by Tseng et al. [ALENEX'19, (2019), pp. 92--106] and parallel Rake-Compress (RC) Trees by Acar et al. [ESA'20, (2020), pp. 2:1--2:23]. Both however are randomized and work efficient in expectation. Several downstream results that use these data structures (and indeed to the best of our knowledge, all known work-efficient parallel batch-dynamic graph algorithms) are therefore also randomized.
In this work, we give the first deterministic work-efficient solution to the problem. Our algorithm maintains a parallel RC-Tree on n vertices subject to batches of k edge updates deterministically in worst-case O(k log(1 + n/k)) work and O(log n loglog k) span on the Common-CRCW PRAM. We also show how to improve the span of the randomized algorithm from O(log n log* n) to O(log n).
Lastly, as a result of our new deterministic algorithm, we also derandomize several downstream results that make use of parallel batch-dynamic dynamic trees, previously for which the only efficient solutions were randomized.
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Index Terms
- Deterministic and Low-Span Work-Efficient Parallel Batch-Dynamic Trees
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