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).
