TY - GEN

T1 - Byzantine dispersion on graphs

AU - Molla, Anisur Rahaman

AU - Mondal, Kaushik

AU - Moses, William K.

N1 - Funding Information:
The work of W. K. Moses Jr. was supported, in part, by a Technion fellowship and, in part, by NSF grants, CCF1540512, IIS-1633720, CCF-1717075, and BSF grant 2016419. A. R. Molla is supported, in part, by DST INSPIRE Faculty Research Grant DST/INSPIRE/04/2015/002801, Govt. of India and ISI DCSW/TAC Project (file number E5412).
Publisher Copyright:
© 2021 IEEE.

PY - 2021/5/1

Y1 - 2021/5/1

N2 - This paper considers the problem of Byzantine dispersion and extends previous work along several parameters. The problem of Byzantine dispersion asks: given n robots, up to f of which are Byzantine, initially placed arbitrarily on an n node anonymous graph, design a terminating algorithm to be run by the robots such that they eventually reach a configuration where each node has at most one non-Byzantine robot on it. Previous work solved this problem for rings and tolerated up to n-1 Byzantine robots. In this paper, we investigate the problem on more general graphs. We first develop an algorithm that tolerates up to n-1 Byzantine robots and works for a more general class of graphs. We then develop an algorithm that works for any graph but tolerates a lesser number of Byzantine robots. We subsequently turn our focus to the strength of the Byzantine robots. Previous work considers only 'weak' Byzantine robots that cannot fake their IDs. We develop an algorithm that solves the problem when Byzantine robots are not weak and can fake IDs. Finally, we study the situation where the number of the robots is not n but some k. We show that in such a scenario, the number of Byzantine robots that can be tolerated is severely restricted. Specifically, we show that it is impossible to deterministically solve Byzantine dispersion when k >(k-f).

AB - This paper considers the problem of Byzantine dispersion and extends previous work along several parameters. The problem of Byzantine dispersion asks: given n robots, up to f of which are Byzantine, initially placed arbitrarily on an n node anonymous graph, design a terminating algorithm to be run by the robots such that they eventually reach a configuration where each node has at most one non-Byzantine robot on it. Previous work solved this problem for rings and tolerated up to n-1 Byzantine robots. In this paper, we investigate the problem on more general graphs. We first develop an algorithm that tolerates up to n-1 Byzantine robots and works for a more general class of graphs. We then develop an algorithm that works for any graph but tolerates a lesser number of Byzantine robots. We subsequently turn our focus to the strength of the Byzantine robots. Previous work considers only 'weak' Byzantine robots that cannot fake their IDs. We develop an algorithm that solves the problem when Byzantine robots are not weak and can fake IDs. Finally, we study the situation where the number of the robots is not n but some k. We show that in such a scenario, the number of Byzantine robots that can be tolerated is severely restricted. Specifically, we show that it is impossible to deterministically solve Byzantine dispersion when k >(k-f).

KW - Byzantine faults

KW - Dispersion

KW - Distributed algorithms

KW - Faulty robots

KW - General graphs

KW - Mobile robots

UR - http://www.scopus.com/inward/record.url?scp=85108394221&partnerID=8YFLogxK

U2 - 10.1109/IPDPS49936.2021.00103

DO - 10.1109/IPDPS49936.2021.00103

M3 - Conference contribution

AN - SCOPUS:85108394221

T3 - Proceedings - 2021 IEEE 35th International Parallel and Distributed Processing Symposium, IPDPS 2021

SP - 942

EP - 951

BT - Proceedings - 2021 IEEE 35th International Parallel and Distributed Processing Symposium, IPDPS 2021

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 35th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2021

Y2 - 17 May 2021 through 21 May 2021

ER -