ON THE COMPLEXITY OF DESIGNING OPTIMAL BRANCH-AND-COMBINE CLOCK NETWORKS

Recently, an unconventional clock distribution scheme, called Branch-a nd-Combine (BaC), has been proposed. The scheme is the first to guaran tee constant skew upper bound irrespective of the clocked network's si ze. in BaC clocking, a set of interconnected nodes perform simple proc essing on clock signals such that the path from the source to any node is automatically and adaptively selected such that it is the shortest delay path. The graph underlying a BaC network is constrained by the requirement that each pair of adjacent nodes is in a cycle of length l ess than or equal to k, where k is the feature cycle length. The graph representing such a network is called a BaC(k) graph. The feature cyc le length (k) is an important parameter upon which skew bound and node function depend. In this paper, we study the complexity of the genera l problem of designing a minimum cost BaC network for clocking a data processing network of arbitrary topology such that a certain feature c ycle length is satisfied. We define two versions of the problem, diffe ring in the way we are allowed to place edges in the graph representin g the BaC network. We show that, in both cases, the general optimizati on problem is NP-hard. We also provide efficient heuristic algorithms for both versions of the optimization problem. When k = 2, the two ver sions of the optimization problem become the same and can he solved in polynomial time. For k = 3, the complexity is still unknown.