VLSI Physical Design Automation
1. KL algorithm: consider the following netlist NL1. Assume that the first gate is the source, and
gate area is all 1.
NL1: n1 = a–b–c, n2 = b–d–e–f, n3 = c–f–g, n4 = a-g, n5 = d-e–h, n6 = f–h
a) Model the netlist with an edge-weighted undirected graph G1. The edge weight is 1/(k-1)
where k is the number of gates, e.g., 1/2 for n1 and 1/3 for n2
b) Given an initial partition P1 = {a,b,c,d | e,f,g,h} of G1, perform a single pass of KL
algorithm. Give the cutsize after each swap. What are the initial, final, and best cutsizes?
2. FM algorithm
a) Model NL1 with a non-weighted hypergraph H1.
b) Given an initial partition P1 (from 1b) of H1, calculate the initial cell gain and setup
buckets for block 0 and 1.
c) Perform a single pass of FM algorithm based on the area constraint [3, 5] (i.e., min is 3
and max is 5 for either side). Ties should be broken in alphabetical order. Give the cutsize
after each move (you don’t need to draw the buckets for each move). What are the initial,
final, and best cutsizes?
3. hMetis algorithm
a) Perform Edge Coarsening on NL1 and derive the corresponding coarsened netlist. Name
clusters Ci. Visit gates in alphabetical order, and coarsen edges based on its weight. Break
ties (with the same weight) based on alphabetical order, i.e., a-c before a-d.
b) Perform Hyperedge Coarsening on NL1 and derive the corresponding coarsened netlist.
Visit nets based on their weights, and break ties based on their indices, i.e., visit n4 before
n6
c) Perform Modified Hyperedge Coarsening on NL1 and derive the corresponding coarsened
netlist. Visit nets based on their weights, and break ties based on their indices, i.e., visit n4
before n6.
4. FBB algorithm
a) Model NL1 with a flow network, where (s,t) = (a,h). The edge label should follow
flow/capacity format.
b) Compute an augmenting path and the maximum amount of flow that can be pushed on it.
Update the flow network after the additional flow.
5. Compare the runtime and space (memory) complexity of the KL, FM, hMetis, and FBB
algorithms.
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