Multi-Server Multi-Function Distributed Computation

Area of Science:

• Distributed Computing and Information Theory

Background:

• Distributed computation frameworks enable complex task execution across multiple servers.
• Quantifying communication costs is crucial for optimizing distributed systems.
• Existing methods may not fully capture the complexities of multi-task, multi-server environments.

Purpose of the Study:

• To establish communication cost upper bounds for multi-server, multi-task distributed computation.
• To analyze these bounds across diverse data statistics, function classes, and data placements.
• To introduce and apply Körner's characteristic graph approach to this framework.

Main Methods:

• Application of Körner's characteristic graph approach to model data and function structures.
• Derivation of general communication cost upper bounds.
• Specialized analysis for cyclic dataset placement and linearly separable/multi-linear functions.

Main Results:

• Established communication cost upper bounds for various configurations in distributed computing.
• Demonstrated significant gains over existing methods for specific scenarios (cyclic placement, linear/multi-linear functions).
• Validated the effectiveness of Körner's characteristic graph approach in this domain.

Conclusions:

• Körner's characteristic graph approach provides a powerful tool for analyzing distributed computation costs.
• The derived bounds offer valuable insights for optimizing communication efficiency.
• The study highlights potential for substantial performance improvements in practical distributed systems.