GRIP: Global Routing via Integer Programming

Abstract

Abstract-This work introduces GRIP, a global routing technique via integer programming. GRIP optimizes wirelength and via cost directly without going through a traditional layer assignment phase. Candidate routes spanning all the metal layers are generated using a linear programming pricing phase that formally accounts for the impact of existing candidate routes when generating new ones. To make an integer-programmingbased approach applicable for today's large-scale global routing instances, the original problem is decomposed into smaller subproblems corresponding to rectangular subregions on the chip together with their net assignments. Route fragments of nets that fall in adjacent subproblems are connected in a flexible manner. In case of overflow, GRIP applies a second-phase optimization that explicitly minimizes overflow. By using integer programming in an effective manner, GRIP obtains high-quality solutions. Specifically, for the ISPD 2007 and 2008 benchmarks, GRIP obtains an average improvement in wirelength and via cost of 9.23% and 5.24%, respectively, when compared to the best result in the open literature.

Placement: From Wirelength to Detailed Routability

“…CGRIP [43] uses integer programming (IP) in global routing, which gives high quality global routing solution in a reasonable amount of time. FastRoute [44] features very short runtime by using congestion-driven and via-aware Steiner tree construction followed by layer assignment.…”

Power-Driven Global Routing for Multisupply Voltage Domains

“…Integer programming allows obtaining a higherquality solution compared to using heuristics as shown in [6]. However, it is not considered a suitable algorithmic venue for large-sized industry circuits.…”

“…This two-step procedure of generating candidate routes and then running branch and bound is commonly known as price and branch [8,9]. The price and branch procedure was recently applied to solve the GR problem for WL improvement [6]. We apply the same procedure for power improvement.…”

“…The discussed pricing procedure is similar to [6]. However, it differs in the pricing condition and the way edge weights are set up.…”

“…Please note, the main difference between our decomposition procedure and [6] is the use of the initial WL-optimized solution to fix the terminal locations on the subregion boundaries and thus avoid later connecting adjacent subproblems.…”