Parallel Algorithms for Zero-One Supply-Demand Problems.

A technique that yields fast parallel algorithms for several zero-one supply-demand problems is presented. NC algorithms are given for the following related problems: (1) Given a sequence of supplies a1,⋯,an and demands b1,⋯,bm, construct a zero-one flow pattern satisfying these constraints, where every supply vertex can send at most one unit of flow to each demand vertex. (2) Given a sequence of positive and negative integers summing to zero, representing supplies and demands, respectively, construct a zero-one flow pattern so that the net flow out of (into) each vertex is its supply (demand), where every vertex can send at most one unit of flow to every other vertex. (3) Construct a digraph without self-loops with specified in- and out-degrees. The results are extended to the case where the input represents upper bounds on supplies and lower bounds on demands.