Skip to main content

The cost of limited communication bandwidth in distributed computing

Periodic Reporting for period 2 - BANDWIDTH (The cost of limited communication bandwidth in distributed computing)

Reporting period: 2019-12-01 to 2021-05-31

Distributed systems underlie many modern technologies, a prime example being the Internet. The ever-increasing abundance of distributed systems necessitates their design and usage to be backed by strong theoretical foundations.

A major challenge that distributed systems face is the lack of a central authority, which brings many aspects of uncertainty into the environment, in the form of unknown network topology or unpredictable dynamic behavior. A practical restriction of distributed systems, which is at the heart of this project, is the limited bandwidth available for communication between the network components.

A central family of distributed tasks is that of local tasks, which are informally described as tasks which are possible to solve by sending information through only a relatively small number of hops in the network. A cornerstone example is the need to break symmetry and provide a better utilization of resources, which can be obtained by the task of producing a valid coloring of the nodes given some small number of colors. Amazingly, there are still huge gaps between the known upper and lower bounds for the complexity of many local tasks. This holds even if one allows powerful assumptions of unlimited bandwidth. While some known algorithms indeed use small messages, the complexity gaps are even larger compared to the unlimited bandwidth case. This is not a mere coincidence, and in fact the existing theoretical infrastructure is provably incapable of giving stronger lower bounds for many local tasks under limited bandwidth.

This project zooms in on this crucial spot in the theory of distributed computing, namely, the study of local tasks under limited bandwidth. The goal of this research is to produce fast algorithms for fundamental distributed local tasks under restricted bandwidth, as well as understand their limitations by providing lower bounds.
We have obtained fast algorithms for subgraph-finding problems, in which the nodes of the distributed network need to detect instances of a certain type of subgraph. Prime examples are triangles or larger cliques, as well as small cycles. As a main methodology for this, we showed how to multiply sparse matrices fast, as well as compute other tasks over space inputs, which we eventually leveraged towards subgraph finding. In addition, we characterized the bandwidth needed for such tasks in dynamic setting, in which the input graph continuously changes over time.

We designed algorithms for symmetry-breaking problems, a prime example being reconfiguration of maximal independent sets (MIS). Moreover, we have designed fast algorithms for many variants of the classic coloring problem, and we obtained fast derandomization results, which resulted in fast deterministic MIS algorithms.

We addressed local optimization, and towards this goal we designed fast algorithms for approximating minimum vertex cover and minimum dominating sets on power graphs. Our research has also yielded fast algorithms for global optimization problems such as spanners and connectivity augmentation problems under restricted bandwidth. Furthermore, we studied hardness of local approximation and obtained various lower bounds, which also include novel techniques for these restricted bandwidth settings.

We have managed to make important connections to additional restricted bandwidth settings, showing connections between various settings in which the common thread is that the communication bandwidth is limited.
In all of our objectives there are still many open questions and our goal is to design even faster algorithms whenever possible for various local tasks in distributed settings of limited bandwidth. In addition, a current line of work we are pursuing is about a newly introduced hybrid model, in which some communication is local and cheap, but some is global and hence needs to adhere to severe bandwidth limitations. We already have new algorithms for fast distance computations in this model, and we expect to obtain much more progress for this type of distributed networks. Another line of work which we expect to make progress on is a better understanding of local optimization and approximation tasks. Our goal is to fill in the complexity gaps that exist for fundamental problems, or to be able to characterize a common hardness.