TY - GEN

T1 - Pebble Guided Near Optimal Treasure Hunt in Anonymous Graphs

AU - Gorain, Barun

AU - Mondal, Kaushik

AU - Nayak, Himadri

AU - Pandit, Supantha

N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

PY - 2021/1/1

Y1 - 2021/1/1

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(Dlog Δ) pebbles to find the treasure in a graph G in time O(Dlog Δ+ log 3Δ), 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 an almost matching lower bound of Ω(Dlog Δ) 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(Dlog Δ) pebbles to find the treasure in a graph G in time O(Dlog Δ+ log 3Δ), 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 an almost matching lower bound of Ω(Dlog Δ) on time of the treasure hunt using any number of pebbles.

KW - Anonymous graph

KW - Mobile agent

KW - Pebbles

KW - Treasure hunt

UR - http://www.scopus.com/inward/record.url?scp=85111412372&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-79527-6_13

DO - 10.1007/978-3-030-79527-6_13

M3 - Conference contribution

AN - SCOPUS:85111412372

SN - 9783030795269

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 222

EP - 239

BT - Structural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings

A2 - Jurdziński, Tomasz

A2 - Schmid, Stefan

PB - Springer Science and Business Media Deutschland GmbH

T2 - 28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021

Y2 - 28 June 2021 through 1 July 2021

ER -