Constructing Large Matchings via Query Access to a Maximal Matching Oracle

Khalil, Lidiya Khalidah binti; Konrad, Christian

doi:10.4230/lipics.fsttcs.2020.26

Cited by 1 publication

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“…Various algorithms are known for computing a (1 − )-approximation to Maximum Matching by repeatedly computing maximal matchings in subgraphs of the input graph (e.g. [2,8,15,22,25,29]). In order to implement these algorithms in the BB(k) model, we need to make sure that the parties know which of their edges are contained in each of the respective subgraphs.…”

Section: Upper Boundsmentioning

confidence: 99%

Robust Lower Bounds for Graph Problems in the Blackboard Model of Communication

Konrad,

Robinson,

Zamaraev

2021

Preprint

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We give lower bounds on the communication complexity of graph problems in the multi-party blackboard model. In this model, the edges of an -vertex input graph are partitioned among parties, who communicate solely by writing messages on a shared blackboard that is visible to every party. We show that any non-trivial graph problem on -vertex graphs has blackboard communication complexity Ω( ) bits, even if the edges of the input graph are randomly assigned to the parties. We say that a graph problem is non-trivial if the output cannot be computed in a model where every party holds at most one edge and no communication is allowed. Our lower bound thus holds for essentially all key graph problems relevant to distributed computing, including Maximal Independent Set (MIS), Maximal Matching, (Δ + 1)-coloring, and Dominating Set. In many cases, e.g., MIS, Maximal Matching, and (Δ + 1)-coloring, our lower bounds are optimal, up to poly-logarithmic factors.

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Section: Upper Boundsmentioning

confidence: 99%