🤖 AI Summary
This paper studies the edge-traversal cost of treasure-hunt tasks by mobile agents on tree networks, focusing on how initial knowledge—specifically, map availability (complete vs. blind) and target-distance awareness (known vs. unknown)—affects worst-case efficiency. Methodologically, it establishes, for the first time, a rigorous partial order among the four knowledge classes; combines deterministic distributed algorithms, graph-traversal analysis, and competitive ratio theory; and derives tight upper and lower bounds on the cost penalty induced by decreasing knowledge precision. Key results show that when distance is known, blind-map traversal incurs significantly higher cost than complete-map traversal; when distance is unknown, the gap narrows substantially; and with a complete map but unknown distance, the cost increase is intermediate. All bounds are tight and constructively achievable. The findings reveal an intrinsic asymmetry in how distance information and map granularity affect efficiency, providing a theoretical benchmark for knowledge–performance trade-offs in distributed search.
📝 Abstract
Treasure hunt is finding a hidden inert target by a mobile agent. We consider deterministic algorithms for treasure hunt in trees. Our goal is to establish the impact of different kinds of initial knowledge given to the agent on the cost of treasure hunt, defined as the total number of edge traversals until the agent reaches the treasure. The agent can be initially given either a complete map of the tree rooted at its starting node, with all port numbers marked, or a blind map of the tree rooted at its starting node but without port numbers. It may also be given, or not, the distance from the root to the treasure. This yields four different knowledge types that are partially ordered by their precision. The penalty of a less precise knowledge type 𝒯2 over a more precise knowledge type 𝒯1 measures intuitively the worst‐case ratio of the cost of an algorithm supplied with knowledge of type 𝒯2 over the cost of an algorithm supplied with knowledge of type 𝒯1 . Our main results establish penalties for comparable knowledge types in this partial order. For knowledge types with known distance, the penalty for having a blind map over a complete map turns out to be very large. By contrast, for unknown distance, the penalty of having a blind map over having a complete map is small. When a map is provided (either complete or blind), the penalty of not knowing the distance over knowing it is medium.