Description
A technique which yields fast parallel algorithms for several zero-one supply-demand problems is presented. We give NC algorithms 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.
(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.
We extend our results to the case where the input represents upper bounds on supplies and lower bounds on demands.