TY - JOUR

T1 - Pebble guided optimal treasure hunt in anonymous graphs

AU - Gorain, Barun

AU - Mondal, Kaushik

AU - Nayak, Himadri

AU - Pandit, Supantha

N1 - Funding Information:
The authors acknowledge the support of Science and Engineering Research Board (SERB), Department of Science and Technology, Govt. of India (grant no. CRG/2020/005964 ). Barun Gorain also acknowledges the partial support of Indian Institute of Technology Research initiation grant. Finally, the authors would like to thank the anonymous referees for their helpful comments, which helped to improve the manuscript substantially.
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/6/24

Y1 - 2022/6/24

N2 - We study the problem of treasure hunt in a graph by a mobile agent. The nodes in the graph are anonymous and the edges at any node v of degree deg(v) are labeled arbitrarily as 0,1,…,deg(v)−1. A mobile agent, starting from a node, must find a stationary object, called treasure that is located on an unknown node at a distance D from its initial position. The agent finds the treasure when it reaches the node where the treasure is present. The time of treasure hunt is defined as the number of edges the agent visits before it finds the treasure. The agent does not have any prior knowledge about the graph or the position of the treasure. An Oracle, that knows the graph, the initial position of the agent, and the position of the treasure, places some pebbles on the nodes, at most one per node, of the graph to guide the agent towards the treasure. We target to answer the question: what is the fastest possible treasure hunt algorithm regardless of the number of pebbles are placed? We show an algorithm that uses O(DlogΔ) pebbles to find the treasure in a graph G in time O(DlogΔ), where Δ is the maximum degree of a node in G and D is the distance from the initial position of the agent to the treasure. We show a matching lower bound of Ω(DlogΔ) on time of the treasure hunt using any number of pebbles.

AB - We study the problem of treasure hunt in a graph by a mobile agent. The nodes in the graph are anonymous and the edges at any node v of degree deg(v) are labeled arbitrarily as 0,1,…,deg(v)−1. A mobile agent, starting from a node, must find a stationary object, called treasure that is located on an unknown node at a distance D from its initial position. The agent finds the treasure when it reaches the node where the treasure is present. The time of treasure hunt is defined as the number of edges the agent visits before it finds the treasure. The agent does not have any prior knowledge about the graph or the position of the treasure. An Oracle, that knows the graph, the initial position of the agent, and the position of the treasure, places some pebbles on the nodes, at most one per node, of the graph to guide the agent towards the treasure. We target to answer the question: what is the fastest possible treasure hunt algorithm regardless of the number of pebbles are placed? We show an algorithm that uses O(DlogΔ) pebbles to find the treasure in a graph G in time O(DlogΔ), where Δ is the maximum degree of a node in G and D is the distance from the initial position of the agent to the treasure. We show a matching lower bound of Ω(DlogΔ) on time of the treasure hunt using any number of pebbles.

KW - Anonymous graph

KW - Deterministic algorithms

KW - Mobile agent

KW - Pebbles

KW - Treasure hunt

UR - http://www.scopus.com/inward/record.url?scp=85129839770&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2022.04.011

DO - 10.1016/j.tcs.2022.04.011

M3 - Article

AN - SCOPUS:85129839770

SN - 0304-3975

VL - 922

SP - 61

EP - 80

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -