Periodic Reporting for period 3 - BANDWIDTH (The cost of limited communication bandwidth in distributed computing)
Periodo di rendicontazione: 2021-06-01 al 2022-11-30
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 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.