Solving ANTS with loneliness detection and constant memory

In 2012, Feinerman et al. introduced the Ants Nearby Treasure Search (ANTS) problem [1]. In this problem, k non-communicating agents with unlimited memory, initially located at the origin, try to locate a treasure distance D from the origin. They show that if the agents know k, then the treasure can be located in the optimal O(D+ D²/k) steps. Furthermore, they show that without knowledge of k, the agents need [omega]((D + D²/k) - log¹+[epsilon] k) steps for some [epsilon] > 0 to locate the treasure. In 2014, Emek et al. studied a variant of the problem in which the agents use only constant memory but are allowed a small amount of communication [2]. Specifically, they allow an agent to read the state of any agent sharing its cell. In this paper, we study a variant of the problem similar to that in [2], but where the agents have even more limited communication. Specifically, the only communication is loneliness detection, in which an agent in able to sense whether it is the only agent located in its current cell. To solve this problem we present an algorithm HYBRID-SEARCH, which locates the treasure in O(D - log k + D² /k) steps in expectation. While this is slightly slower than the straightforward lower bound of [omega](D + D² /k), it is faster than the lower bound for agents locating the treasure without communication.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• O'Brien, Casey (Casey M.)

Advisor dc:contributor.advisor

• Nancy Lynch.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/106119

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/106119