TY - GEN
T1 - Edge Exploration of a Graph by Mobile Agent
AU - Dhar, Amit Kumar
AU - Gorain, Barun
AU - Mondal, Kaushik
AU - Patra, Shaswati
AU - Singh, Rishi Ranjan
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this paper, we study the problem of edge exploration of an n node graph by a mobile agent. The nodes of the graph are unlabeled, and the ports at a node of degree d are arbitrarily numbered. A mobile agent, starting from some node, has to visit all the edges of the graph and stop. The time of the exploration is the number of edges the agent traverses before it stops. The task of exploration can not be performed even for a class of cycles if no additional information, called advice, is provided to the agent a priori. Following the paradigm of algorithms with advice, this priori information is provided to the agent by an Oracle in the form of a binary string. The Oracle knows the graph, but does not have the knowledge of the starting point of the agent. In this paper, we consider the following two problems of edge exploration. The first problem is: “how fast is it possible to explore an n node graph regardless of the size of advice provided to the agent?” We show a lower bound ofon exploration time to answer the above question. Next, we show the existence of an time algorithm with advice. The second problem then asks the following question: “what is the smallest advice that needs to be provided to the agent in order to achieve time?” We show a lower bound on size of the advice, for any, to answer the above question.
AB - In this paper, we study the problem of edge exploration of an n node graph by a mobile agent. The nodes of the graph are unlabeled, and the ports at a node of degree d are arbitrarily numbered. A mobile agent, starting from some node, has to visit all the edges of the graph and stop. The time of the exploration is the number of edges the agent traverses before it stops. The task of exploration can not be performed even for a class of cycles if no additional information, called advice, is provided to the agent a priori. Following the paradigm of algorithms with advice, this priori information is provided to the agent by an Oracle in the form of a binary string. The Oracle knows the graph, but does not have the knowledge of the starting point of the agent. In this paper, we consider the following two problems of edge exploration. The first problem is: “how fast is it possible to explore an n node graph regardless of the size of advice provided to the agent?” We show a lower bound ofon exploration time to answer the above question. Next, we show the existence of an time algorithm with advice. The second problem then asks the following question: “what is the smallest advice that needs to be provided to the agent in order to achieve time?” We show a lower bound on size of the advice, for any, to answer the above question.
KW - Advice
KW - Algorithm
KW - Exploration
KW - Graph
KW - Mobile agent
UR - http://www.scopus.com/inward/record.url?scp=85078535455&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-36412-0_12
DO - 10.1007/978-3-030-36412-0_12
M3 - Conference contribution
AN - SCOPUS:85078535455
SN - 9783030364113
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 142
EP - 154
BT - Combinatorial Optimization and Applications - 13th International Conference, COCOA 2019, Proceedings
A2 - Li, Yingshu
A2 - Cardei, Mihaela
A2 - Huang, Yan
PB - Springer
T2 - 13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019
Y2 - 13 December 2019 through 15 December 2019
ER -