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On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy
On The Difficulty Of Manhattan Channel Routing, Ronald I. Greenberg, Joseph Jaja, Sridhar Krishnamurthy
Ronald Greenberg
We show that channel routing in the Manhattan model remains difficult even when all nets are single-sided. Given a set of n single-sided nets, we consider the problem of determining the minimum number of tracks required to obtain a dogleg-free routing. In addition to showing that the decision version of the problem isNP-complete, we show that there are problems requiring at least d+Omega(sqrt(n)) tracks, where d is the density. This existential lower bound does not follow from any of the known lower bounds in the literature.
Lower Bounds On The Area Of Finite-State Machines, M. J. Foster, Ronald I. Greenberg
Lower Bounds On The Area Of Finite-State Machines, M. J. Foster, Ronald I. Greenberg
Ronald Greenberg
There are certain straightforward algorithms for laying out finite-state machines. This paper shows that these algorithm are optimal in the worst case for machines with fixed alphabets. That is, for any s and k, there is a deterministic finite-state machine with s states and k symbols such that any layout algorithm requires Ω(ks log s) area to lay out its realization. Similarly, any layout algorithm requires Ω(ks^2) area in the worst case for nondeterministic finite-state machines with s states and k symbols.