In this paper we study distributed algorithms on massive graphs where links represent a particular relationship between nodes (for instance, nodes may represent phone numbers and links may indicate telephone calls). Since such graphs are massive they need to be processed in a distributed way. When computing graph-theoretic properties, nodes become natural units for distributed computation. Links do not necessarily represent communication channels between the computing units and therefore do not restrict the communication flow. Our goal is to model and analyze the computational power of such distributed systems where one computing unit is assigned to each node. Communication takes place on a whiteboard where each node is allowed to write at most one message. Every node can read the contents of the whiteboard and, when activated, can write one small message based on its local knowledge. When the protocol terminates its output is computed from the final contents of the whiteboard. We describe four synchronization models for accessing the whiteboard. We show that message size and synchronization power constitute two orthogonal hierarchies for these systems. We exhibit problems thatseparate these models, i.e., that can be solved in one model but not in a weaker one, even with increased message size. These problems are related to maximal independent set and connectivity. We also exhibit problems that require a given message size independently of the synchronization model.

Authors and Affiliations

1. LIFO, Université d’Orléans, Orléans, France

   Florent Becker & Ioan Todinca

2. Inria Paris - LIAFA, Université Paris Diderot, Paris, France

   Adrian Kosowski

3. DIM-CMM (UMI 2807 CNRS), Universidad de Chile, Santiago, Chile

   Martin Matamala & Ivan Rapaport

4. CNRS, I3S, Sophia-Antipolis, Inria & Univ. Nice Sophia-Antipolis, Nice, France

   Nicolas Nisse

5. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile

   Karol Suchan

6. Faculty of Applied Mathematics, AGH - University of Science and Technology, Kraków, Poland

   Karol Suchan

Corresponding author

Correspondence toMartin Matamala.

This paper is the union of two preliminary versions appeared in the proceedings of SPAA 2012 (Allowing each node to communicate only once in a distributed system: shared whiteboard models) and IPDPS 2011 (Adding a referee to an interconnection network: What can (not) be computed in one round?). It has been partially supported by programs Fondap and Basal-CMM (M.M., I.R., K.S.), Fondecyt 1100192 (M.M.), 1130061 (I.R.), FP7 STREP EULER (N.N.), ANR AGAPE (I.T.), ANR Displexity (A.K.), NCN under contract DEC-2011/02/A/ST6/00201 (A.K.), Ecos-Conicyt C09E04 (M.M., I.R., I.T.), Ecos-Sud Chili C12E03 (N.N, K.S.) and Associated Team Inria AlDyNet (N.N, K.S.).

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