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Binary Stretch Embedding of Weighted Graphs Analysis


Core Concepts
Introducing and studying the binary stretch embedding problem for edge-weighted graphs.
Abstract
The article introduces the binary stretch embedding problem for edge-weighted graphs, closely related to addressing problems. It discusses isometric hypercube embedding and its applications. The use of Hadamard codes and linear programming techniques to find upper and lower bounds for certain classes of graphs is explored. Results are applied to Lee metric codes, deriving improved bounds. The paper also outlines an integer programming formulation and its linear relaxation for the problem.
Stats
Isometric hypercube embedding introduced by Firsov in 1965. Minimum length of binary code containing n codewords and minimum distance d. Maximum size of Lee metric codes derived from results in the paper. Hadamard codes used to find upper bounds in linear programming formulations.
Quotes

Key Insights Distilled From

by Javad B. Ebr... at arxiv.org 03-15-2024

https://arxiv.org/pdf/2403.09311.pdf
Binary Stretch Embedding of Weighted Graphs

Deeper Inquiries

Practical Implications of Binary Stretch Embedding

Binary stretch embedding has practical implications beyond theoretical graph theory. One significant application is in the field of network design and optimization. By efficiently assigning binary addresses to vertices in a graph, communication networks can be structured more effectively, leading to improved data transmission speeds and reduced latency. This optimization can enhance the overall performance of communication systems, making them more reliable and efficient.

Impact of Addressing Problems on Real-World Applications

Addressing problems play a crucial role in real-world applications like communication systems. In these systems, assigning unique addresses to different components or nodes is essential for routing messages accurately and ensuring seamless connectivity. By solving addressing problems efficiently, we can improve the reliability and speed of data transmission within networks. Additionally, addressing problems are fundamental in designing error-correcting codes for data storage and transmission applications.

Extension of Findings on Lee Metric Codes

The findings on Lee metric codes provide valuable insights into error-correcting code scenarios beyond their specific application. These findings can be extended to various error-correction techniques used in telecommunications, computer networks, and digital communications. By understanding the relationship between code size, minimum distance, and other parameters derived from Lee metric codes research, we can optimize error-correction algorithms for better performance in diverse applications such as secure data transfer protocols or fault-tolerant computing systems.
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