Becker, F., Kosowski, A., Matamala, M., Nisse, N., Rapaport, I., Suchan, K., et al. (2015). Allowing each node to communicate only once in a distributed system: shared whiteboard models. Distrib. Comput., 28(3), 189–200.
Abstract: 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 graphtheoretic 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 that separate 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.

Matamala, M., & Moreno, E. (2009). Minimum Eulerian circuits and minimum de Bruijn sequences. Discret. Math., 306(17), 5298–5304.
Abstract: Given a digraph (directed graph) with a labeling on its arcs, We Study the problem of finding the Eulerian circuit of lexicographically minimum label. We prove that this problem is NPcomplete in general, but if the labelling is locally injective (arcs going out from each vertex have different labels), we prove that it is solvable in linear time by giving an algorithm that Constructs this circuit. When this algorithm is applied to a de Bruijn graph, it obtains the de Bruijn sequences with lexicographically minimum label. (C) 2007 Elsevier B.V. All rights reserved.
