New bounds for the longest edge of a tree in a VLSI layout

Abstract

In the last three years many results were published about graph layout in VLSI. One aspect of graph layout is the minimization of the longest edge; for this problem Bhatt and Leiserson (1982) recently demonstrated a new technique to shorten the longest edge, and they thus achieved an upper bound of O(sqrt{N}/log N) for trees. Unfortunately, no good universal lower bounds exist. This paper presents a general techniques for proving lower bounds for trees. A second technique to embed trees is presented, which provides really good upper bounds for the maximal edge length in relation to the disposable area.