arXiv subjects

Giuseppe Antonio Di Luna

Publications and source records attributed to Giuseppe Antonio Di Luna.

21 records · Page 2Linked to original sources

arXiv2016

Population Protocols with Faulty Interactions: the Impact of a Leader

We consider the problem of simulating traditional population protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner's state during an interaction), which in turn may be detectable or undetectable. We focus on the impact of a leader, and we give a complete characterization of the models in which the presence of a unique leader in the system allows the construction of simulators: when simulations are possible, we give explicit protocols; when they are not, we give proofs of impossibility. Specifically, if each agent has only a finite amount of memory, the simulation is possible only if there are no omission faults. If agents have an unbounded amount of memory, the simulation is possible as long as omissions are detectable. If an upper bound on the number of omissions involving the leader is known, the simulation is always possible, except in the one-way model in which one side is unable to detect the interaction.

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arXiv2016

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

In this paper we investigate the computational power of Population Protocols (PP) under some unreliable and/or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of PP, is the loss by one or both parties of the information transmitted in an interaction. The failure may or may not be detected by either party. On the other hand, in one-way models, communication happens only in one direction: only one of the two agents can change its state depending on both agents' states, and the other agent may or may not be aware of the interaction. These notions can be combined, obtaining one-way protocols with (possibly detectable) omission failures. A general question is what additional power is necessary and sufficient to completely overcome the weakness of one-way protocols and enable them to simulate two-way protocols, with and without omission failures. As a basic feature, a simulator needs to implement an atomic communication of states between two agents; this task is further complicated by the anonymity of the agents, their lack of knowledge of the system, and the limited amount of memory that they may have. We provide the first answers to these questions by presenting and analyzing several simulators, i.e., wrapper protocols converting any protocol for the standard two-way model into one running on a weaker one.

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arXiv2015

Investigating the Cost of Anonymity on Dynamic Networks

In this paper we study the difficulty of counting nodes in a synchronous dynamic network where nodes share the same identifier, they communicate by using a broadcast with unlimited bandwidth and, at each synchronous round, network topology may change. To count in such setting, it has been shown that the presence of a leader is necessary. We focus on a particularly interesting subset of dynamic networks, namely \textit{Persistent Distance} - ${\cal G}($PD$)_{h}$, in which each node has a fixed distance from the leader across rounds and such distance is at most $h$. In these networks the dynamic diameter $D$ is at most $2h$. We prove the number of rounds for counting in ${\cal G}($PD$)_{2}$ is at least logarithmic with respect to the network size $|V|$. Thanks to this result, we show that counting on any dynamic anonymous network with $D$ constant w.r.t. $|V|$ takes at least $D+ Ω(\text{log}\, |V| )$ rounds where $Ω(\text{log}\, |V|)$ represents the additional cost to be payed for handling anonymity. At the best of our knowledge this is the fist non trivial, i.e. different from $Ω(D)$, lower bounds on counting in anonymous interval connected networks with broadcast and unlimited bandwith.

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