This paper shows howalarge class of interprocedural dataflow-analysis problems can be solved precisely in polynomial time. The only restrictions are that the set of dataflowfacts is a finite set, and that the dataflowfunctions distribute overthe confluence operator (either union or intersection). This class of problems includes---but is not limited to---the classical separable problems (also known as "gen/kill" or "bit-vector" problems)---e.g.,reaching definitions, available expressions, and live variables. In addition, the class of problems that our techniques handle includes manynon-separable problems, including trulylive variables, copyconstant propagation, and possibly-uninitialized variables. Anovelaspect of our approach is that an interprocedural dataflow-analysis problem is transformed into a special kind of graph-reachability problem (reachability along interprocedurally realizable paths). The paper presents three polynomial-time algorithms for the realizable-path reachability problem: an exhaustive version, a second exhaustive version that may be more appropriate in the incremental and/or interactive context, and a demand version. The first and third of these algorithms are asymptotically faster than the best previously known realizable-path reachability algorithm. An additional benefit of our techniques is that theylead to improvedalgorithms for twoother kinds of interproceduralanalysis problems: interprocedural flow-sensitive side-effect problems (as studied by Callahan) and interprocedural program slicing (as studied by Horwitz, Reps, and Binkley). CR Categories and Subject Descriptors: D.3.4 [Programming Languages]: Processors - compilers, optimization;E.1 [Data