Solving ANTS with loneliness detection and constant memory
Author(s)
O'Brien, Casey (Casey M.)
DownloadFull printable version (7.200Mb)
Alternative title
Solving Ants Nearby Treasure Search with loneliness detection and constant memory
Other Contributors
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Advisor
Nancy Lynch.
Terms of use
Metadata
Show full item recordAbstract
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.
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015. Cataloged from PDF version of thesis. Includes bibliographical references (page 105).
Date issued
2015Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer SciencePublisher
Massachusetts Institute of Technology
Keywords
Electrical Engineering and Computer Science.