An Exact Formula for the Expected Wire Length Between Two Randomly Chosen Terminals (1994)
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author = {David Lazoff And and David M. Lazoff and Alan T. Sherman},
title = {An Exact Formula for the Expected Wire Length Between Two Randomly Chosen Terminals},
institution = {},
year = {1994}
}
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Abstract:
Introduction Motivated by geometric problems in VLSI design, we recently derived a formula for the expected Euclidean distance between two randomly-chosen points uniformly distributed in an arbitrary rectangle [10]. Although we subsequently discovered that Ghosh [6, 7] had published a solution in 1943 in the Calcutta Statistical Association Bulletin, we would like to make the formula conveniently available to modern practitioners in a simple, directly usable form. Oblivious to Ghosh's work, and overwhelmed by algebraic difficulties of the problem, previous computer science researchers have resorted to special cases, asymptotic bounds, and numerical approximations. Using elementary techniques, we give an exact closed-form solution involving square roots, natural logarithms, and rational functions of the two rectangle dimensions. The Two-Terminal Wire Length Problem (WLP 2 ) is to compute the expected Euclidean distance be
