On the Complexity of the Minimum and Maximum Global Snapshot Problems

Derivang the min imum and maximum global snapshots is very useful f o r some error detection problems in distributed programs. Several researchers, e.g., Groselj, Chen and W u , have shown that the min imum and maximum global snapshot problems are lineart ime reducible to the max imum constant-ratio network flow (MCNF) problem, here defined as the well-known maximum network flow problem with m = O ( n ) , where m is the number of edges and n is the number of vertices i n the given flow network. I n this paper we show in a reverse way that the M C N F problem is also linear-time reducible t o these global snapshot problems. Thus, we can conclude that the global snapshot problems are “as di6cul t as” the M C N F problem i n terms of t ime complexity.