Biological systems can share and collectively process information to yield emergent effects, despite inherent noise in communication. While man-made systems often employ intricate structural solutions to overcome noise, the structure of many biological systems is more amorphous. It is not well understood how communication noise may affect the computational repertoire of such groups. To approach this question we consider the basic collective task of rumor spreading, in which information from few knowledgeable sources must reliably flow into the rest of the population. In order to study the effect of communication noise on the ability of groups that lack stable structures to efficiently solve this task, we consider a noisy version of the uniform PULL model. We prove a lower bound which implies that, in the presence of even moderate levels of noise that affect all facets of the communication, no scheme can significantly outperform the trivial one in which agents have to wait until directly interacting with the sources. Our results thus show an exponential separation between the uniform PUSH and PULL communication models in the presence of noise. Such separation may be interpreted as suggesting that, in order to achieve efficient rumor spreading, a system must exhibit either some degree of structural stability or, alternatively, some facet of the communication which is immune to noise. We corroborate our theoretical findings with a new analysis of experimental data regarding recruitment in Cataglyphis niger desert ants.
The computational study of abstract systems composed of simple individuals that interact using highly restricted and stochastic interactions has recently been gaining considerable attention in the community of theoretical computer science. Popular models include population protocols @cite_28 , which typically consider constant size individuals that interact in pairs (using constant size messages) in random communication patterns, and the beeping model @cite_36 , which assumes a fixed network with extremely restricted communication. Our model also falls in this framework as we consider the @math model @cite_25 @cite_21 @cite_22 with constant size messages. So far, despite interesting works that consider different fault-tolerant contexts @cite_19 @cite_7 , most of the progress in this framework considered noiseless scenarios.
@cite_22 @cite_7 @cite_28 @cite_36 @cite_21 @cite_19 @cite_25
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This article studies self-stabilization in networks of anonymous, asynchronously interacting nodes where the size of the network is unknown. Constant-space protocols are given for Dijkstra-style round-robin token circulation, leader election in rings, two-hop coloring in degree-bounded graphs, and establishing consistent global orientation in an undirected ring. A protocol to construct a spanning tree in regular graphs using O(log D) memory is also given, where D is the diameter of the graph. A general method for eliminating nondeterministic transitions from the self-stabilizing implementation of a large family of behaviors is used to simplify the constructions, and general conditions under which protocol composition preserves behavior are used in proving their correctness. Population protocols are used as a theoretical model for a collection (or population) of tiny mobile agents that interact with one another to carry out a computation. The agents are identically programmed finite state machines. Input values are initially distributed to the agents, and pairs of agents can exchange state information with other agents when they are close together. The movement pattern of the agents is unpredictable, but subject to some fairness constraints, and computations must eventually converge to the correct output value in any schedule that results from that movement. This framework can be used to model mobile ad hoc networks of tiny devices or collections of molecules undergoing chemical reactions. This chapter surveys results that describe what can be computed in various versions of the population protocol model. Computational and biological systems are often distributed so that processors (cells) jointly solve a task, without any of them receiving all inputs or observing all outputs. Maximal independent set (MIS) selection is a fundamental distributed computing procedure that seeks to elect a set of local leaders in a network. A variant of this problem is solved during the development of the fly’s nervous system, when sensory organ precursor (SOP) cells are chosen. By studying SOP selection, we derived a fast algorithm for MIS selection that combines two attractive features. First, processors do not need to know their degree; second, it has an optimal message complexity while only using one-bit messages. Our findings suggest that simple and efficient algorithms can be developed on the basis of biologically derived insights. We describe and analyze a 3-state one-way population protocol for approximate majority in the model in which pairs of agents are drawn uniformly at random to interact. Given an initial configuration of x's, y's and blanks that contains at least one non-blank, the goal is for the agents to reach consensus on one of the values x or y. Additionally, the value chosen should be the majority non-blank initial value, provided it exceeds the minority by a sufficient margin. We prove that with high probability n agents reach consensus in O(n log n) interactions and the value chosen is the majority provided that its initial margin is at least ω(√n log n). This protocol has the additional property of tolerating Byzantine behavior in o(√n) of the agents, making it the first known population protocol that tolerates Byzantine agents. Turning to the register machine construction from [2], we apply the 3-state approximate majority protocol and other techniques to speed up the per-step parallel time overhead of the simulation from O(log4 n) to O(log2 n). To increase the robustness of the phase clock at the heart of the register machine, we describe a consensus version of the phase clock and present encouraging simulation results; its analysis remains an open problem. Whru a dilt lhSC is replicated at, many sites2 maintaining mutual consistrnry among t,he sites iu the fac:e of updat,es is a signitirant problem. This paper descrikrs several randomized algorit,hms for dist,rihut.ing updates and driving t,he replicas toward consist,c>nc,y. The algorit Inns are very simple and require few guarant,ees from the underlying conllllunicat.ioll system, yc+ they rnsutc t.hat. the off( c t, of (‘very update is evcnt,uwlly rf+irt-ted in a11 rq1ica.s. The cost, and parformancc of t,hr algorithms arc tuned I>? c oosing appropriat,c dist,rilMions in t,hc randoinizat,ioii step. TIN> idgoritlmls ilr(’ c*los *ly analogoIls t,o epidemics, and t,he epidcWliolog)litc , ilitlh iii Illld rsti4lldill tlicir bc*liavior. One of tlW i$,oritlims 11&S brc>n implrmcWrd in the Clraringhousr sprv(brs of thr Xerox C’orporat c Iiitcrnc4, solviiig long-standing prol>lf lns of high traffic and tlatirl>ilsr inconsistcllcp.