The f-fault-tolerant connectivity labeling (f-FTC labeling) is a scheme of assigning each vertex and edge with a small-size label such that one can determine the connectivity of two vertices s and t under the presence of at most f faulty edges only from the labels of s, t, and the faulty edges. This paper presents a new deterministic f-FTC labeling scheme attaining O(f2polylog(n))-bit label size and a polynomial construction time, which settles the open problem left by Dory and Parter (in: Proceedings of the 2021 ACM symposium on principles of distributed computing (PODC), pp 445–455, 2021). The key ingredient of our construction is to develop a deterministic counterpart of the graph sketch technique by Ahn et al. (in: Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on principles of database systems (PODS), pp 5–14, 2012), via some natural connection with the theory of error-correcting codes. This technique removes one major obstacle in de-randomizing the Dory–Parter scheme. The whole scheme is obtained by combining this technique with a new deterministic graph sparsification algorithm derived from the seminal ϵ-net theory, which is also of independent interest. As byproducts, our result deduces the first deterministic fault-tolerant approximate distance labeling scheme with a non-trivial performance guarantee and an improved deterministic fault-tolerant compact routing. The authors believe that our new technique is potentially useful in the future exploration of more efficient FTC labeling schemes and other related applications based on graph sketches.

How to efficiently and reliably spread information in a system is one of the most fundamental problems in distributed computing. Recently, inspired by biological scenarios, several works focused on identifying the minimal communication resources necessary to spread information under faulty conditions. Here we study the self-stabilizing bit-dissemination problem, introduced by Boczkowski, Korman, and Natale in [SODA 2017]. The problem considers a fully-connected network of nagents, with a binary world of opinions, one of which is called correct. At any given time, each agent holds an opinion bit as its public output. The population contains a source agent which knows which opinion is correct. This agent adopts the correct opinion and remains with it throughout the execution. We consider the basic PULL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {PULL}$$\\end{document} model of communication, in which each agent observes relatively few randomly chosen agents in each round. The goal of the non-source agents is to quickly converge on the correct opinion, despite having an arbitrary initial configuration, i.e., in a self-stabilizing manner. Once the population converges on the correct opinion, it should remain with it forever. Motivated by biological scenarios in which animals observe and react to the behavior of others, we focus on the extremely constrained model of passive communication, which assumes that when observing another agent the only information that can be extracted is the opinion bit of that agent. We prove that this problem can be solved in a poly-logarithmic in n number of rounds with high probability, while sampling a logarithmic number of agents at each round. Previous works solved this problem faster and using fewer samples, but they did that by decoupling the messages sent by agents from their output opinion, and hence do not fit the framework of passive communication. Moreover, these works use complex recursive algorithms with refined clocks that are unlikely to be used by biological entities. In contrast, our proposed algorithm has a natural appeal as it is based on letting agents estimate the current tendency direction of the dynamics, and then adapt to the emerging trend.

This special issue of Distributed Computing is based on papers that originally appeared as extended abstracts in the Proceedings of the 40th Symposium on Principles of distributed computing (PODC 2021), held as a virtual conference, and in the Proceedings of the 35th International Symposium on Distributed Computing (DISC 2021), held as a hybrid event, both virtually and in Freiburg, Germany. The papers for the Special Issue were chosen by the respective Program Committees from the regular papers presented at the symposium, based on their quality and representation of the spectrum of topics encompassed by the B Hagit Attiya

We consider a stateless ‘amnesiac’ variant of the stateful distributed network flooding algorithm, expanding on our conference papers [PODC’19, STACS’20]. Flooding begins with a set of source ‘initial’ nodes I seeking to broadcast a message M in rounds, in a network represented by an undirected graph (G, E) with set of nodes G and edges E. In every round, nodes with M send M to all neighbours from which they did not receive M in the previous round. Nodes do not remember earlier rounds, raising the possibility that M circulates indefinitely. Stateful flooding overcomes this by nodes recording every message circulated and ignoring M if received again. This overhead was assumed to be necessary. We show that almost optimal broadcast can still be achieved without this overhead. We prove that amnesiac flooding terminates on every finite graph and derive sharp bounds for termination times. Define (G, E) to be I-bipartite if the quotient graph, contracting all nodes in I to a single node, is bipartite. We prove that, if d is the diameter and e(I) the eccentricity of the set I, flooding terminates in e(I) rounds if (G, E) is I-bipartite and j rounds with e(I) < jle e(I)+d+1 le 2d +1 if (G, E) is non I-bipartite. The separation in the termination times can be used for distributed discovery of topologies/distances in graphs. Termination is guaranteed if edges are lost during flooding but not, in general, if there is a delay at an edge. However, the cases of single-edge fixed delays of duration tau rounds in single-source bipartite graphs terminate by round 2d+tau -1, and all cases of multiple-edge fixed delays in multiple-source cycles terminate.