DeepAI
Log In Sign Up

Finding Subgraphs in Highly Dynamic Networks

09/17/2020
by   Keren Censor-Hillel, et al.
0

In this paper we consider the fundamental problem of finding subgraphs in highly dynamic distributed networks - networks which allow an arbitrary number of links to be inserted / deleted per round. We show that the problems of k-clique membership listing (for any k≥ 3), 4-cycle listing and 5-cycle listing can be deterministically solved in O(1)-amortized round complexity, even with limited logarithmic-sized messages. To achieve k-clique membership listing we introduce a very useful combinatorial structure which we name the robust 2-hop neighborhood. This is a subset of the 2-hop neighborhood of a node, and we prove that it can be maintained in highly dynamic networks in O(1)-amortized rounds. We also show that maintaining the actual 2-hop neighborhood of a node requires near linear amortized time, showing the necessity of our definition. For 4-cycle and 5-cycle listing, we need edges within hop distance 3, for which we similarly define the robust 3-hop neighborhood and prove it can be maintained in highly dynamic networks in O(1)-amortized rounds. We complement the above with several impossibility results. We show that membership listing of any other graph on k≥ 3 nodes except k-clique requires an almost linear number of amortized communication rounds. We also show that k-cycle listing for k≥ 6 requires Ω(√(n) / log n) amortized rounds. This, combined with our upper bounds, paints a detailed picture of the complexity landscape for ultra fast graph finding algorithms in this highly dynamic environment.

READ FULL TEXT

page 1

page 2

page 3

page 4

12/11/2021

A tight bound for the clique query problem in two rounds

We consider a problem introduced by Feige, Gamarnik, Neeman, Rácz and Te...
05/18/2018

Distributed Computation in the Node-Congested Clique

The Congested Clique model of distributed computing, which was introduce...
04/25/2019

Distributed Detection of Cliques in Dynamic Networks

This paper provides an in-depth study of the fundamental problems of fin...
08/22/2022

Fault-Tolerant Graph Realizations in the Congested Clique

In this paper, we study the graph realization problem in the Congested C...
07/23/2018

Random Sampling Applied to the MST Problem in the Node Congested Clique Model

The Congested Clique model, proposed by Lotker et al. [SPAA'03, SICOMP'0...
11/08/2018

Approximate Neighbor Counting in Radio Networks

For many distributed algorithms, neighborhood size is an important param...
01/19/2023

Efficient Computation in Congested Anonymous Dynamic Networks

An "anonymous dynamic network" is a network of indistinguishable process...