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<p>In a connected graph space <i>G</i> (a discrete structure/a point space), the navigation of an AI agent (assumed to be a point robot) can be taken into place with the help of fewest landmarks. The sense of distance in <i>G</i> provides a platform to choose such fewest landmarks, which is called a metric basis of <i>G</i>. This concept of graph theory allows an AI agent to locate itself uniquely for navigation. As a metric basis of <i>G</i> is not unique, so it is natural to ask which of the specified metric bases of <i>G</i> is the best landmarks provider by using them for a rapid and distraction-free navigation of an AI agent. Such a metric basis of <i>G</i> is said to be an optimal metric basis. In this paper, we address the aforesaid problem by originating a novel approach of metric differential. We consider all those graph spaces in which landmarks already have been observed by inspecting their metric basis. We use our new approach to explore optimal metric basis out of all the existing metric basis of these graph spaces.</p>

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The Metric Differential: An Efficient Approach for a Navigating Agent to Rapidly Locate Itself in a Graph Space Through Optimal Landmarks

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Niaz Ahmad,
  • Muhammad Salman,
  • Faisal Ali

摘要

In a connected graph space G (a discrete structure/a point space), the navigation of an AI agent (assumed to be a point robot) can be taken into place with the help of fewest landmarks. The sense of distance in G provides a platform to choose such fewest landmarks, which is called a metric basis of G. This concept of graph theory allows an AI agent to locate itself uniquely for navigation. As a metric basis of G is not unique, so it is natural to ask which of the specified metric bases of G is the best landmarks provider by using them for a rapid and distraction-free navigation of an AI agent. Such a metric basis of G is said to be an optimal metric basis. In this paper, we address the aforesaid problem by originating a novel approach of metric differential. We consider all those graph spaces in which landmarks already have been observed by inspecting their metric basis. We use our new approach to explore optimal metric basis out of all the existing metric basis of these graph spaces.