  In this paper, a new graph partitioning problem is introduced. The depth of
each part is constrained, i.e., the node count in the longest path of the
corresponding sub-graph is no more than a predetermined positive integer value
p. An additional constraint is enforced such that each part contains only nodes
selected from consecutive levels in the graph. The problem is therefore
transformed into a Depth-bounded Levelized Graph Partitioning (DLGP) problem,
which is solved optimally using a dynamic programming algorithm. As an example
application, we have shown that DLGP can effectively generate timing-correct
circuit solutions for Single Flux Quantum (SFQ) logic, which is a
magnetic-pulse-based, gate-level pipelined superconductive computing fabric.
Experimental results confirm that DLGP generates circuits with considerably
lower path balancing overheads compared with a baseline full-path-balancing
approach. For example, the balancing overhead (a critical measure of quality
metric) for the SFQ circuit realization in terms of D-Flip-Flop count is
reduced by 3.61 times on average for 10 benchmark circuit, given p=5.
