Abstract
The problem of detecting negative weight cycles in a graph is examined
in the context of the dynamic graph structures that arise in
the process of high level synthesis (HLS). The concept of
adaptive negative cycle detection is introduced, in which a
graph changes over time and negative cycle detection needs to be done
periodically, but not necessarily after every individual change. We
present an algorithm for this problem, based on a novel extension of
the well-known Bellman-Ford algorithm that allows us to adapt existing
cycle information to the modified graph, and show by experiments that
our algorithm significantly outperforms previous incremental approaches
for dynamic graphs. In terms of applications, the adaptive technique
leads to a very fast implementation of Lawlers algorithm for the
computation of the maximum cycle mean (MCM) of a graph, especially for
a certain form of sparse graph. Such sparseness often occurs in
practical circuits and systems, as demonstrated, for example, by the
ISCAS 89/93 benchmarks. The application of the adaptive technique to
design-space exploration (synthesis) is also demonstrated by
developing automated search techniques for scheduling iterative
data-flow graphs.
