An ADD-based algorithm for shortest path back-tracing of large graphs

Symbolic computation techniques play a fundamental role in these days logic synthesis and formal hardware veriication algorithms. Recently, Algebraic Decision Diagrams, i.e., BDD's with a set of constant values diierent than the set f0; 1g, have been used to solve general purpose problems, such as matrix multiplication, shortest path calculation, and solution of linear systems, as well as logic synthesis and formal veriication problems, such as timing analysis, re-synthesis for low-power, probabilistic analysis of FSM's, and state space decomposition for approximate FSM traversal. ADD-based procedures for single-source and all-pairs shortest path weight calculation have appeared to be very eeective for the manipulation of large graphs (over 10 27 vertices and 10 36 edges). However, for those procedures to be applicable to real problems, for example ow network problems, computing only shortest path weights is not enough; what it is needed is an algorithm that, given the weight of a shortest path between two vertices of a graph, actually determines the sequence of vertices belonging to the shortest path. In this paper, we propose a symbolic algorithm for shortest path back-tracing which exploits the compactness of the ADD data structure to handle large graphs.