A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Distributed snapshots: determining global states of distributed systems
ACM Transactions on Computer Systems (TOCS)
Time, clocks, and the ordering of events in a distributed system
Communications of the ACM
Bounded and Minimum Global Snapshots
IEEE Parallel & Distributed Technology: Systems & Technology
Detection of Weak Unstable Predicates in Distributed Programs
IEEE Transactions on Parallel and Distributed Systems
Efficient Detection of Restricted Classes of Global Predicates
WDAG '95 Proceedings of the 9th International Workshop on Distributed Algorithms
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Deriving the minimum and maximum global snapshots is very useful for some error detection problems in distributed programs. Several researchers, e.g., Groselj, Chen and Wu, have shown that the minimum and maximum global snapshot problems are linear-time reducible to the maximum constant-ratio network flow (MCNF) problem, here defined as the well-known maximum network flow problem with m = \Theta(n), where m is the number of edges and n is the number of vertices in the given flow network. In this paper we show in a reverse way that the MCNF problem is also linear-time reducible to these global snapshot problems. Thus, we can conclude that the global snapshot problems are ``as difficult as" the MCNF problem in terms of time complexity.