Distributed Planar Reachability in Nearly Optimal Time

@inproceedings{Parter2020DistributedPR,
  title={Distributed Planar Reachability in Nearly Optimal Time},
  author={Merav Parter},
  booktitle={DISC},
  year={2020}
}
We present nearly optimal distributed algorithms for fundamental reachability problems in planar graphs. In the single-source reachability problem given is an n-vertex directed graph G = (V, E) and a source node s, it is required to determine the subset of nodes that are reachable from s in G. We present the first distributed reachability algorithm for planar graphs that runs in nearly optimal time of Õ(D) rounds, where D is the undirected diameter of the graph. This improves the complexity of… Expand

Figures from this paper

On Sparsity Awareness in Distributed Computations
TLDR
This work establishes a new framework by developing an intermediate auxiliary model which is weak enough to be successfully simulated in the classic congest model given low mixing time, and proves that despite imposing harsh restrictions, this artificial model allows balancing massive data transfers with a maximal utilization of bandwidth. Expand

References

SHOWING 1-10 OF 35 REFERENCES
Parallel Reachability in Almost Linear Work and Square Root Depth
TLDR
This paper provides a parallel algorithm that given any n-node m-edge directed graph and source vertex s computes all vertices reachable from s with Õ(m) work and n^{1/2 + o(1)} depth with high probability in n and is the first nearly optimal algorithm for general graphs whose diameter is Ω(n^δ) for any constant δ. Expand
Reachability and Shortest Paths in the Broadcast CONGEST Model
TLDR
A stronger lower bound of $\Omega(\sqrt{n}\,)$ for the single-source shortest path problem for unweighted directed graphs that holds even when the diameter of the underlying network is $2$ is proved, which is the first lower bound that achieves this problem. Expand
Brief Announcement: Distributed Single-Source Reachability
In the directed single-source reachability problem, input is a directed graph G=(V, E) and a source node s, and the objective is to identify nodes t for which there is a directed path in G from s toExpand
Near-Optimal Distributed DFS in Planar Graphs
TLDR
This is the first sublinear-time distributed DFS algorithm, improving on a three decades-old O(n) algorithm of Awerbuch (1985), which remains the best known for general graphs. Expand
Improved algorithms for min cut and max flow in undirected planar graphs
TLDR
These are the first algorithms breaking the O(n log n) barrier for those two problems, which has been standing for more than 25 years, and the first known non-trivial dynamic algorithm for min st-cut and max st-flow. Expand
Distributed exact shortest paths in sublinear time
TLDR
An all-pairs shortest paths algorithm that requires O(n5/3 #183; log2/3 n) time, even for b = 1, for all values of D, and provides an improved bound, compared to the unit-bandwidth case. Expand
Distributed Algorithms for Planar Networks I: Planar Embedding
TLDR
This paper presents the first (non-trivial) distributed planar embedding algorithm that matches the trivial lower bound of Omega(D) up to a log n factor. Expand
Distributed approximation algorithms for weighted shortest paths
TLDR
The time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O (log n) bandwidth restriction on edges is studied to find a sublinear-time algorithm with almost optimal solution. Expand
Distributed Algorithms for Planar Networks II: Low-Congestion Shortcuts, MST, and Min-Cut
TLDR
Low-congestion shortcuts for (near-)planar networks are introduced, and their power is demonstrated by using them to obtain near-optimal distributed algorithms for problems such as Minimum Spanning Tree or Minimum Cut, in planar networks. Expand
Round- and Message-Optimal Distributed Graph Algorithms
TLDR
This paper provides algorithms that are simultaneously round- and message-optimal for a number of well-studied distributed optimization problems, including MST, Approximate Min-Cut and Approximates Single Source Shortest Paths, among others. Expand
...
1
2
3
4
...