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Coordination in constrained and natural distributed systems

Periodic Reporting for period 1 - CoCoNat (Coordination in constrained and natural distributed systems)

Reporting period: 2019-06-01 to 2021-05-31

The design of scalable and reliable distributed systems relies on communication-efficient synchronization algorithms, as nodes in the network need to coordinate their activities in a collective fashion.

This project investigated the complexity of fundamental distributed synchronization and coordination tasks in constrained distributed systems with limited computational and communicational capabilities. These systems arise in the context of contemporary networking applications, but also in novel application areas such as molecular computing and biocomputing.

The main focus of the project was to understand how limitations, such as small communication bandwidth, asynchronous computation, or unreliable and unpredictable interaction patterns, influence the solvability and complexity of basic synchronization and coordination tasks in different models of distributed computing.

During the course of the project, several new analysis techniques were developed. These have been used to show both (1) new improved algorithms and (2) complementary impossibility results for several coordination problems in various models of distributed computing. For example, we showed new results regarding on reaching approximate agreement in a fault-tolerant manner, studied how to efficiently deal with dynamically changing inputs in large-scale communication networks, and gave new algorithms for leader election and majority tasks in spatially-structured biomolecular systems.
Input-dynamic graph algorithms. In many distributed communication networks, the structure of the communication topology remains fairly static (i.e. the physical communication links between nodes), but instead only the input in the network (i.e. routing demands) may dynamically change over time.
Motivated by this, we investigated the following questions: if processes in the network already have an existing solution to a network problem and some of the local inputs of the processes change, can the existing solution be updated efficiently in a distributed manner?

We developed a new model of batch dynamic CONGEST model to study input-dynamic network problems in a distributed setting, where the nodes can communicate only a limited number of bits per time unit across a communication channel. In this setting, we established new complexity results regarding the maintenance of a minimum spanning tree and various subgraph detection problems in the distributed input-dynamic setting. The results were published in the ACM SIGMETRICS 2021 conference.

Approximate agreement. Approximate agreement is a fundamental problem related to various distributed tasks ranging from distributed clock synchronization to robot gathering tasks. We obtained new results on approximate agreement tasks, the set of input values have spatial structure represented by a graph. In this problem, each process is given an input value that corresponds to a node on the graph. The goal is to output nodes on the graph so that (1) all output nodes are adjacent in the graph and (2) every output node lies on a shortest path between some input nodes.
A key set of results in this area was to identify new conditions when the problem admits a distributed algorithm and when the problem is provably impossible to solve a wait-free algorithm. More precisely, we identified a new class of graphs, where approximate agreement is provably impossible to solve by a wait-free algorithm. Conversely, we gave a new algorithm that solves the problem on a large class of graphs. These results were published in the International Colloquium on Structural Information and Communication Complexity SIROCCO 2021.

Distributed load balancing. In many networking applications, it is necessary to assign work units (e.g. requests from clients) to different servers in the network. To efficiently utilize the network, it is desirable to allocate these work units in a balanced manner. We gave improved upper and lower bounds on the complexity of the stable assignment and locally optimal semi-matching problems in the LOCAL model of distributed computation. These results were presented in the ACM Symposium on Parallelism in Algorithms and Architectures SPAA 2021.

Graphical population protocols. Population protocols are a popular model of biomolecular computation, where computation proceeds via pairwise interactions between nodes in a system. In this model, we are given a graph G in which every node represents a computational element (e.g. a molecule, cell or a simple device) and a scheduler picks uniformly at random two nodes connected by an edge to interact.
A vast majority of the research in this model has focused on well-mixed system in which the interaction graph G is a clique. In this project, we investigated a spatially-structured version of this model, where G may be an arbitrary regular graph.

During this project, we developed a new general transformation of clique-based protocols into graphical protocols whose time and space complexity are bounded by the expansion properties of the underlying interaction graph G. In particular, this shows that graphs with good expansion properties admit coordination protocols that are efficient both in terms of time complexity (time to reach a desired configuration) and space complexity (the total number of states used by any node).
The project has advanced the state of the art in distributed coordination tasks in various models of distributed systems. Beyond technical advancements in developing new algorithms and mathematical proof techniques, the results have potential to have a wider industrial and societal impact in the long term.

The results regarding input-dynamic network algorithms may have significant future impact in developing self-driving networks, which automatically maintain and re-configure themselves according to dynamic changes and needs in the network. In particular, there is an ongoing need for developing scalable and efficient network management protocols given the increasing volume of traffic in modern communication networks and data centers. Efficient management of these networks has the potential to save considerably amounts of energy and reduce emissions generated by the operation of these networks.
Graphical population protocols model computation among individuals that interact in stochastic and unpredictable patterns. Such interactions occur in various kinds of engineered and natural systems. For example, the model can be used to study both biomolecular computation, but also computation in ad hoc mobile network. Thus, understanding how the spatial structure of the interaction graph affects complexity of protocols can provide better insight in how to develop protocols for such systems.