Tolerating linear number of faults in networks of bounded degree

In [7], Dwork et al. proposed a new paradigm for fault tolerant distributed computing termed azmost everywhere agreement. While all other fault tolerance paradigms require networks of high connectivity to tolerate substantial number of faults, it was shown in [7] that the new paradigm can be achieved even on bounded degree networks, as long as the number of faults is bounded by O(n/ log n), where n is the size of the network. A major problem that was left open in [7] is whether almost everywhere agreement can be achieved on bounded degree networks in the presence of up to O(n) faulty nodes (processors). In this work we answer this question in the affirmative. As in [7], our solution is based on a general technique for simulating on a bounded degree network an algorithm designed for the complete network. Each communication round of the complete *IBM Almaden Research Center, San Jose, CA 95120, and Department of Applied Mathematics, The Weizmann Institute of Science, Rehovot, Israel. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires e fee and/or specific permission. PoDC ‘92-81921B.C. @ 1992 ACM 0-89791 -496-11921000810083 . ..$1 .50 network protocol is simulated by a logarithmic number of communication rounds, and with a polynomial number of messages.