On Memory, Communication, and Synchronous Schedulers When Moving and Computing
We investigate the computational power of distributed systems whose autonomous computational entities, called robots, move and operate in the 2-dimensional Euclidean plane in synchronous Look-Compute-Move (LCM) cycles. Specifically, we focus on the power of persistent memory and that of explicit communication, and on their computational relationship.
In the most common model, OBLOT, the robots are oblivious (no persistent memory) and silent (no explicit means of communication). In contrast, in the LUMI model, each robot is equipped with a constant-sized persistent memory (called light), visible to all the robots; hence, these luminous robots are capable in each cycle of both remembering and communicating. Since luminous robots are computationally more powerful than the standard oblivious one, immediate important questions are about the individual computational power of persistent memory and of explicit communication. In particular, which of the two capabilities, memory or communication, is more important? in other words, is it better to remember or to communicate ?
In this paper we address these questions, focusing on two sub-models of LUMI: FSTA, where the robots have a constant-size persistent memory but are silent; and FCOM, where the robots can communicate a constant number of bits but are oblivious. We analyze the relationship among all these models and provide a complete exhaustive map of their computational relationship. Among other things, we prove that communication is more powerful than persistent memory under the fully synchronous scheduler Fsynch, while they are incomparable under the semi-synchronous scheduler Ssynch.
Look-Compute-Move
Oblivious mobile robots
Robots with lights
Memory versus Communication
Moving and Computing
Theory of computation~Distributed algorithms
25:1-25:17
Regular Paper
This research was partly supported by NSERC through the Discovery Grant program, by Prof. Flocchini’s University Research Chair, by JSPS KAKENHI No. 17K00019, and by Japan Science and Technology Agency (JST) SICORP Grant#JPMJSC1806.
Paola
Flocchini
Paola Flocchini
EECS, University of Ottawa, Canada
Nicola
Santoro
Nicola Santoro
School of Computer Science, Carleton University, Canada
Koichi
Wada
Koichi Wada
Faculty of Science and Engineering, Hosei University, Japan
10.4230/LIPIcs.OPODIS.2019.25
N. Agmon and D. Peleg. Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM Journal on Computing, 36(1):56-82, 2006.
H. Ando, Y. Osawa, I. Suzuki, and M. Yamashita. A distributed memoryless point concergence algorithm for mobile robots with limited visivility. IEEE Transactions on Robotics and Automation, 15(5):818-828, 1999.
S. Bhagat and K. Mukhopadhyaya. Optimum algorithm for mutual visibility among asynchronous robots with lights. In Proc. of the 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pages 341-355, 2017.
Z. Bouzid, S. Das, and S. Tixeuil. Gathering of mobile robots tolerating multiple crash Faults. In the 33rd Int. Conf. on Distributed Computing Systems (ICDCS), pages 334-346, 2013.
D. Canepa and M. Gradinariu Potop-Butucaru. Stabilizing flocking via leader election in robot networks. In Proc. of the 10th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pages 52-66, 2007.
S. Cicerone, Di Stefano, and A. Navarra. Gathering of robots on meeting-points. Distributed Computing, 31(1):1-50, 2018.
M. Cieliebak, P. Flocchini, G. Prencipe, and N. Santoro. Distributed computing by mobile robots: Gathering. sicomp, 41(4):829-879, 2012.
R. Cohen and D. Peleg. Convergence properties of the gravitational algorithms in asynchronous robot systems. sicomp, 34(15):1516-1528, 2005.
S. Das, P. Flocchini, G. Prencipe, N. Santoro, and M. Yamashita. The power of lights: synchronizing asynchronous robots using visible bits. In Proc. of the 32nd International Conference on Distributed Computing Systems (ICDCS), pages 506-515, 2012.
S. Das, P. Flocchini, G. Prencipe, N. Santoro, and M. Yamashita. Autonomous mobile robots with lights. Theoretical Computer Science, 609:171-184, 2016.
G.A. Di Luna, P. Flocchini, S.G. Chaudhuri, F. Poloni, N. Santoro, and G. Viglietta. Mutual visibility by luminous robots without collisions. Information and Computation, 254(3):392-418, 2017.
G.A. Di Luna and G. Viglietta. Robots with Lights. Chapter 11 of [12], pages 252-277, 2019.
P. Flocchini, G. Prencipe, and N. Santoro (Eds). Distributed Computing by Mobile Entities. Springer, 2019.
P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Hard tasks for weak robots: the role of common knowledge in pattern formation by autonomous mobile robots. In Proc. of 10th International Symposium on Algorithms and Computation (ISAAC), pages 93-102, 1999.
P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Gathering of asynchronous robots with limited visibility. tcs, 337(1-3):147-169, 2005.
P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Arbitrary pattern formation by asynchronous oblivious robots. tcs, 407:412-447, 2008.
P. Flocchini, N. Santoro, G. Viglietta, and M. Yamashita. Rendezvous with Constant Memory. tcs, 621:57-72, 2016.
N. Fujinaga, Y. Yamauchi, H. Ono, S. Kijima, and M. Yamashita. Pattern formation by oblivious asynchronous mobile robots. sicomp, 44(3):740-785, 2015.
V. Gervasi and G. Prencipe. Coordination without communication: The case of the flocking problem. Discrete Applied Mathematics, 144(3):324-344, 2004.
A. Hériban, X. Défago, and S. Tixeuil. Optimally gathering two robots. In Proc. of the 19th Int. Conference on Distributed Computing and Networking (ICDCN), pages 1-10, 2018.
T. Izumi, S. Souissi, Y. Katayama, N. Inuzuka, X. Défago, K. Wada, and M. Yamashita. The gathering problem for two oblivious robots with unreliable compasses. sicomp, 41(1):26-46, 2012.
T. Okumura, K. Wada, and X. Défago. Optimal Rendezvous ℒ-Algorithms for Asynchronous Mobile Robots with External-Lights. In Proc. of the 22nd Int. Conference on Principles of Distributed Systems (OPODIS), pages 24:1-24:16, 2018.
T. Okumura, K. Wada, and Y. Katayama. Brief Announcement: Optimal asynchronous Rendezvous for mobile robots with lights. In Proc. of the 19th Int. Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pages 484-488, 2017.
D. Peleg. Distributed coordination algorithms for mobile robot swarms: New directions and challenges. In Proc. of 7th International Workshop on Distributed Computing (IWDC), pages 1-12, 2005.
G. Sharma, R. Alsaedi, C. Bush, and S. Mukhopadyay. The complete visibility problem for fat robots with lights. In Proc. of the 19th International Conference on Distributed Computing and Networking (ICDCN), pages 21:1-21:4, 2018.
S. Souissi, T. Izumi, and K. Wada. Oracle-based flocking of mobile robots in crash-recovery model. In Proc. of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pages 683-697, 2009.
I. Suzuki and M. Yamashita. Distributed anonymous mobile robots: Formation of geometric patterns. sicomp, 28:1347-1363, 1999.
S. Terai, K. Wada, and Y. Katayama. Gathering problems for autonomous mobile robots with lights. arXiv.org, cs(ArXiv:1811.12068), 2018.
G. Viglietta. Rendezvous of two robots with visible bits. In 10th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS), pages 291-306, 2013.
M. Yamashita and I. Suzuki. Characterizing geometric patterns formable by oblivious anonymous mobile robots. tcs, 411(26-28):2433-2453, 2010.
Y. Yamauchi, T. Uehara, S. Kijima, and M. Yamashita. Plane formation by synchronous mobile robots in the three-dimensional euclidean space. Journal of the ACM (JACM), 64:3(16):16:1-16:43, 2017.
Paola Flocchini, Nicola Santoro, and Koichi Wada
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