Counting the Number of Minimum Roman Dominating Functions of a Graph

📝 Original Info

• Title: Counting the Number of Minimum Roman Dominating Functions of a Graph
• ArXiv ID: 1403.1019
• Date: 2014-03-11
• Authors: Researchers from original ArXiv paper

📝 Abstract

We provide two algorithms counting the number of minimum Roman dominating functions of a graph on n vertices in O(1.5673^n) time and polynomial space. We also show that the time complexity can be reduced to O(1.5014^n) if exponential space is used. Our result is obtained by transforming the Roman domination problem into other combinatorial problems on graphs for which exact algorithms already exist.

💡 Deep Analysis

Deep Dive into Counting the Number of Minimum Roman Dominating Functions of a Graph.

We provide two algorithms counting the number of minimum Roman dominating functions of a graph on n vertices in O(1.5673^n) time and polynomial space. We also show that the time complexity can be reduced to O(1.5014^n) if exponential space is used. Our result is obtained by transforming the Roman domination problem into other combinatorial problems on graphs for which exact algorithms already exist.

📄 Full Content

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