Information-Theoretic Encoding of Graphs

Title: Information-Theoretic Encoding of Graphs

Research Question: Can we develop a methodology for encoding graphs with minimum information-theoretic bit count, while maintaining the ability to reconstruct the graph from the encoding?

Methodology: The researchers propose a fast methodology for encoding graphs with properties (π-graphs) that have information-theoretically minimum bit counts. They use super-additive continuous functions (β(n)) to limit the number of distinct π-graphs. The methodology is applicable to general classes of graphs and focuses on planar graphs.

Results: The researchers provide examples of π-graphs, including planar, directed, undirected, triangulated, biconnected, and labeled graphs. They show that their methodology allows for encoding and decoding of graphs in O(nlogn) time, with bit counts of at most β(n) + o(β(n)).

Implications: This research has significant implications for the field of graph theory and information theory. It provides a novel approach to encoding graphs with minimum bit counts, which can be applied to various graph-based problems. The methodology also leads to the discovery of new applications of small cycle separators of planar graphs, making it a valuable contribution to the existing body of knowledge.

In conclusion, this research proposes a fast methodology for encoding graphs with information-theoretic minimum bit counts. The methodology is applicable to general classes of graphs and focuses on planar graphs. It provides examples of π-graphs and shows that the bit counts are at most β(n) + o(β(n)). The research has significant implications for the field of graph theory and information theory, and it leads to the discovery of new applications of small cycle separators of planar graphs.

Link to Article: https://arxiv.org/abs/0101021v1 Authors: arXiv ID: 0101021v1