# Distributed exact weighted all-pairs shortest paths in near-linear time

@article{Bernstein2018DistributedEW, title={Distributed exact weighted all-pairs shortest paths in near-linear time}, author={Aaron Bernstein and Danupon Nanongkai}, journal={Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing}, year={2018} }

In the distributed all-pairs shortest paths problem (APSP), every node in the weighted undirected distributed network (the CONGEST model) needs to know the distance from every other node using least number of communication rounds (typically called time complexity). The problem admits (1+o(1))-approximation Θ(n)-time algorithm and a nearly-tight Ω(n) lower bound [Nanongkai, STOC’14; Lenzen and Patt-Shamir PODC’15]. For the exact case, Elkin [STOC’17] presented an O(n5/3 log2/3 n) time bound…

## 37 Citations

### Distributed Exact Shortest Paths in Sublinear Time

- Computer ScienceJ. ACM
- 2020

This article provides an all-pairs shortest paths algorithm that requires O(n5/3 ⋅ log 2/3 n) time, even for b = 1, for all values of D, and devise the first algorithm with non-trivial complexity guarantees for computing exact shortest paths in the multipass semi-streaming model of computation.

### Faster Deterministic All Pairs Shortest Paths in Congest Model

- Computer ScienceSPAA
- 2020

A new deterministic algorithm for distributed weighted all pairs shortest paths (APSP) in both undirected and directed graphs is presented, which significantly improves on the deterministic blocker set algorithms in [ARKP18, AR19] by removing an additional n ·|Q| term in the round bound.

### Distributed Weighted All Pairs Shortest Paths Through Pipelining

- Computer Science2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)
- 2019

The techniques in the results simplify some of the procedures in the earlier APSP algorithms for non-negative edge weights in [HNS17, ARKP18], improving results in [Nanongkai14, LP15] that hold only for positive integer weights.

### Distributed edge connectivity in sublinear time

- Computer ScienceSTOC
- 2019

By combining the recent distributed expander decomposition technique of [Chang, Pettie, Zhang, SODA’19] with techniques from the sequential deterministic edge connectivity algorithm of [Kawarabayashi, Thorup, STOC’15], the network can decompose into a sublinear number of clusters with small average diameter and without any mincut separating a cluster (except the “trivial” ones).

### Universally-Optimal Distributed Shortest Paths and Transshipment via Graph-Based L1-Oblivious Routing

- Computer ScienceSODA
- 2022

The construction is simple, solely based on low-diameter decompositions, and—in contrast to all known constructions—directly produces an oblivious flow instead of just an approximation of the optimal flow cost.

### Universally-optimal distributed algorithms for known topologies

- Computer ScienceSTOC
- 2021

This work provides several (equivalent) graph parameters and shows they are tight universal lower bounds for the above problems, fully characterizing their inherent complexity, and implies that algorithms based on the low-congestion shortcut framework match the above lower bound, making them universally optimal if shortcuts are efficiently approximable.

### Undirected (1+𝜀)-shortest paths via minor-aggregates: near-optimal deterministic parallel and distributed algorithms

- Computer ScienceSTOC
- 2022

This paper presents near-optimal deterministic parallel and distributed algorithms for computing (1+eps)-approximate single-source shortest paths in any undirected weighted graph. On a high level, we…

### 16 : 2 A Distributed Algorithm for Directed MinimumWeight Spanning Tree

- Computer Science
- 2019

This paper presents the first sub-quadratic DMST algorithms in the distributed CONGEST network model, where the messages exchanged between the network nodes are bounded in size and uses a distributed single-source shortest-path algorithm for directed graphs as a black box.

### Quantum Distributed Algorithm for the All-Pairs Shortest Path Problem in the CONGEST-CLIQUE Model

- Computer SciencePODC
- 2019

This paper constructs a Õ(n1/4)-round quantum distributed algorithm for the APSP over directed graphs with polynomial weights in the CONGEST-CLIQUE model and shows how to implement multiple quantum searches in parallel without introducing congestions.

### Hardness of Distributed Optimization

- Computer Science, MathematicsPODC
- 2019

This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing tildeΩmega (n2) lower…

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