Constructing lower and upper bounded delay routing trees using linear programming

Abstract

This paper presents a new approach for solving the Lower and Upper Bounded delay routing Tree (LUBT) problem using linear programming. LUBT is a Steiner tree rooted at the source node such that delays from the source to sink nodes lie between the given lower and upper bounds. We show that our proposed method produces minimum cost LUBT for a given topology under a linear delay model. Unlike recent works which control only the difference between the maximum and the minimum source-sink delay, we construct routing trees which satisfy distinct lower and upper bound constraints on the source-sink delays. This formulation exploits all the flexibility that is present in low power and high performance clock routing tree design.