Election and rendezvous with incomparable labels

Abstract

International audienceIn “Can we elect if we cannot compare” (SPAA'03), Barrière, Flocchini, Fraigniaud and Santoro consider a qualitative model of distributed computing, where the labels of the entities are distinct but mutually incomparable. They study the leader election problem in a distributed mobile environment and they wonder whether there exists an algorithm such that for each distributed mobile environment, it either states that the problem cannot be solved in this environment, or it successfully elects a leader. In this paper, we give a positive answer to this question. We also give a characterization of the distributed mobile environments where election and rendezvous can be solved

Rendezvous of Mobile Agents without Agreement on Local Orientation

“…In fact, we show that the problem of RVwA is solvable in exactly those instances where rendezvous with common port numbering is possible. In contrast, in the qualitative model of Barrière et al [4,9] the class of solvable instances is much larger.…”

“…(Step E) Agent r removes the two tokens from its homebase (Step F) Agent r goes to each homebase h, and waits until either there is no token on h, or there is a sleeping agent on h. Constructing an order on equivalence classes: Given any vertex-labelled graph (G, μ), there exists standard procedures for partitioning the vertex set of G to obtain an ordered sequence of equivalence classes that respect the labelling. (See [4,9] for example.) Note that since the agents start with the same labelled graph (G, μ), they compute the same ordered sequence of equivalence classes.…”

“…Our model is similar to the qualitative model of computation [4,9] where the incident edges at a node have distinct labels but the agents do not agree on a total order on these labels (i.e. the labels are said to incomparable).…”

“…On one hand, our model is more general than the anonymous port-to-port network model and on the other hand it is less powerful than qualitative model of Barrière et al. [4,9] where the agents have distinct labels. Our results hold even in the simplest model of communication using identical tokens and in fact, we show that using two tokens per agent is necessary and sufficient for solving the problem.…”

Fault-tolerant simulation of population protocols

“…Each node v i is connected to its two neighbours v i−1 and v i+1 via distinctly labeled ports q i− and q i+ , respectively (all operations on the indices are modulo n); the labeling of the ports may not be globally consistent, thus might not provide an orientation, and the label may not be comparable [14]. The ring is said to be anonymous if the nodes have no distinguishable identifiers, and with landmark if there is a node (the landmark) which is different from all others.…”