A Biological Solution to a Fundamental Distributed Computing Problem

Abstract

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.

The Computational Power of Beeps

“…They motivated this model by noting the continuous model in [11,12,17] was unrealistic and yielded trivial solutions to desynchronization, they then demonstrated how to solve desynchronization without these assumptions. Around this same time, Afek et al [3] described a maximal independent set (MIS) algorithm in a strong version of the discrete beeping model. They argued that something like this algorithm might play a role in the proper distribution of sensory organ precursor cells in fruit fly nervous system development.…”

“…The beeping model of network communication [1][2][3]10,14,19] assumes a collection of computational nodes, connected in a network, that interact by beeping in synchronous rounds. If a node decides to beep in a given round, it receives no feedback from the channel.…”

FrogCOL and FrogMIS: new decentralized algorithms for finding large independent sets in graphs

“…Apart from these three algorithms we also implemented the two randomized algorithms mentioned in [9], which are labelled Rand1 and Rand2 (in the same way as described in [9]). Finally, we also implemented an optimized version (from [23]) of a very recent algorithm published in the Science journal [2]. As this algorithm is inspired by the development of the nervous system of fruitflies, this algorithm is henceforth labelled FruitFly.…”

Natural algorithms and influence systems

“…This paper is based on "Natural Algorithms," which was published in the Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms, 2009, and subsequent work. maximal independent sets in fly brain development 1 , and so on. Consensus, synchronization, and fault tolerance are concepts central to both biology and distributed computing 15,17 .…”

“…Let G t be the (undirected) graph whose edges are the positive entries in P t . With x(t + 1) = P t x(t) and x(0) = x ∈ [0, 1] n , the total s-energy is defined as…”