| Autor: |
Rozhoň, Václav, Grunau, Christoph, Haeupler, Bernhard, Zuzic, Goran, Li, Jason |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this and other shortest-path problems to $\tilde{O}(1)$ Minor-Aggregations. A Minor-Aggregation computes an aggregate (e.g., max or sum) of node-values for every connected component of some subgraph. Our reduction immediately implies: Optimal deterministic parallel (PRAM) algorithms with $\tilde{O}(1)$ depth and near-linear work. Universally-optimal deterministic distributed (CONGEST) algorithms, whenever deterministic Minor-Aggregate algorithms exist. For example, an optimal $\tilde{O}(HopDiameter(G))$-round deterministic CONGEST algorithm for excluded-minor networks. Several novel tools developed for the above results are interesting in their own right: A local iterative approach for reducing shortest path computations "up to distance $D$" to computing low-diameter decompositions "up to distance $\frac{D}{2}$". Compared to the recursive vertex-reduction approach of [Li20], our approach is simpler, suitable for distributed algorithms, and eliminates many derandomization barriers. A simple graph-based $\tilde{O}(1)$-competitive $\ell_1$-oblivious routing based on low-diameter decompositions that can be evaluated in near-linear work. The previous such routing [ZGY+20] was $n^{o(1)}$-competitive and required $n^{o(1)}$ more work. A deterministic algorithm to round any fractional single-source transshipment flow into an integral tree solution. The first distributed algorithms for computing Eulerian orientations. |
| Databáze: |
arXiv |
| Externí odkaz: |
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