Methods and Algorithms for Coupling Reduction

In this work, we develop methods to reduce interconnect delay and noise caused by coupling. First, we introduce a novel problem that deals with coupling the Coupling-Free Routing (CFR) Problem. CFR takes a set of nets and tries to nd a one-bend routing for a subset of nets. A routed net must not couple with any other routed net. We argue that this problem is useful in both global and detailed routing. It guarantees that the routing has minimum delay since the wirelength, number of vias and coupling are minimized. Then, we present an exact algorithm for the CFR decision problem via a transformation to 2-satis ability. The decision problem determines whether the given set of nets is coupling-free routable. Next, we introduce a new type of graph, the implication graph which models the dependencies associated with CFR. Also, we look at some of the properties associated with the graph. Finally, we develop three algorithms to e ciently solve the MaximumCouplingFree Layout (MAX-CFL) problem. Given a set of nets, the problem is de ned as nding a subset of nets that are coupling-free routable. The subset should have maximum size and/or criticality. The criticality of a net can be de ned in a variety of ways e.g. timing slack, wirelength, etc.. The rst algorithm, the greedy algorithm, is a simple, yet e ective method for nding a set of nets which have maximum criticality. The direct forcing algorithm uses the notion of forcing to nd a solution to the MAX-CFL problem. The nal algorithm we present is the implication algorithm. It uses properties associated with the implication graph and consistently nds the best solution in terms of number of nets routed. Our experimental results show that the algorithms work e ectively on real data.