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Memory Conscious Graph Coloring for Context Free Graphs Using Sparse Matrices

Author(s) Raghavendra Prasad Yelisetty
Country United States
Abstract A framework is a conceptual structure composed of a series of components, typically known as nodes or centers, interconnected by links, often termed as connections or pathways. Each connection functions as a conduit between two nodes, representing a relationship or interaction. Frameworks are categorized based on the properties of their components and connections. A directed framework, or digraph, consists of connections with defined directionality, indicating movement from one node to another. In contrast, an undirected framework contains bidirectional connections, symbolizing mutual relationships between connected nodes. In a weighted framework, the links are assigned numerical values, which may represent factors such as cost, strength, or capacity, while an unweighted framework only shows the connections without additional numerical information. Framework labeling refers to the process of assigning unique markers, often represented by colors, to nodes or connections based on certain guidelines. The main objective is to ensure that adjacent components do not share the same marker. This method finds widespread applications in real-world scenarios such as load distribution, problem-solving, and collaborative planning. For example, it is used in timetable management to avoid overlapping events, signal distribution in wireless networks to reduce interference, and even in puzzle solving, such as Sudoku. The colorability of a framework refers to the minimum number of distinct markers required for valid labeling. Depending on its design, a framework might only need two markers (making it bipartite) or more. A common approach for labeling frameworks is the greedy strategy, which iteratively assigns the smallest possible marker not yet used by neighboring nodes. While this provides a quick and simple solution, it does not always result in the smallest number of markers needed. Finding the optimal labeling system, known as the minimal colorability, is a computationally difficult problem classified as NP-complete, indicating that the difficulty increases significantly as the framework grows larger. Despite its computational complexity, framework labeling remains valuable in various fields. In systems engineering, it aids in managing storage in translators to enhance processing speed. In broadcast technology, it reduces frequency clashes by properly assigning signals. Additionally, it plays a crucial role in logistical planning, ensuring the efficient allocation of tasks and resources without conflicts. This paper addresses on reducing the memory consumption using sparse matrix at context free graph coloring.
Keywords Complete graph, null graph, degree, in degree, out degree, edge, bipartite, connected graph , disconnected graph.
Field Computer
Published In Volume 14, Issue 3, July-September 2023
Published On 2023-08-03
Cite This Memory Conscious Graph Coloring for Context Free Graphs Using Sparse Matrices - Raghavendra Prasad Yelisetty - IJSAT Volume 14, Issue 3, July-September 2023.
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