Periodic Reporting for period 4 - BANDWIDTH (The cost of limited communication bandwidth in distributed computing)
Reporting period: 2022-12-01 to 2023-11-30
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.
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 sparse inputs, which we eventually leveraged towards subgraph finding. We further showed how to obtain fast subgraph finding in a deterministic manner, by developing new tools for such distributed settings. In addition, we characterized the bandwidth needed for such tasks in a dynamic setting, in which the input graph continuously changes over time. In a yet harsher dynamic setting which assumes no restrictions at all on the topology changes, we show how to maintain information about all cliques in the network. Many of our results are accompanied by lower bounds, establishing the optimality of many of our algorithms.
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 developed constant-time algorithms for maintaining solutions for symmetry-breaking tasks in the aforementioned highly-dynamic setting.
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. Examples include several highly dynamic settings, a recently introduced hybrid model that combines global and local communication, a distributed quantum setting which models the exchange of qubits rather than bits along communication channels, and more.
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 developed constant-time algorithms for maintaining solutions for symmetry-breaking tasks in the aforementioned highly-dynamic setting.
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. Examples include several highly dynamic settings, a recently introduced hybrid model that combines global and local communication, a distributed quantum setting which models the exchange of qubits rather than bits along communication channels, and more.
We have designed powerful algorithms for fundamental distributed tasks in various bandwidth-restricted settings. All of our algorithms push the state of the art forward, some of them are provably optimal to to lower bounds that we show.
To summarize, this project has made major contributions to advancing the domain of distributed graph algorithms in bandwidth-restricted settings.
To summarize, this project has made major contributions to advancing the domain of distributed graph algorithms in bandwidth-restricted settings.