Pebble Guided Near Optimal Treasure Hunt in Anonymous Graphs

Barun Gorain, Kaushik Mondal, Himadri Nayak, Supantha Pandit

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationStructural Information and Communication Complexity - 28th International Colloquium, SIROCCO 2021, Proceedings
EditorsTomasz Jurdziński, Stefan Schmid
PublisherSpringer Science and Business Media Deutschland GmbH
Pages222-239
Number of pages18
ISBN (Print)9783030795269
DOIs
StatePublished - 1 Jan 2021
Externally publishedYes
Event28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021 - Virtual, Online
Duration: 28 Jun 20211 Jul 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12810 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference28th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2021
CityVirtual, Online
Period28/06/211/07/21

Keywords

  • Anonymous graph
  • Mobile agent
  • Pebbles
  • Treasure hunt

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