On the Construction of Optimal Obstacle-Avoiding Rectilinear Steiner Minimum Trees

Abstract

Abstract-This paper presents an efficient method to solve the obstacle-avoiding rectilinear Steiner tree (OARSMT) problem optimally. Our work is developed based on the GeoSteiner approach in which full Steiner trees (FSTs) are first constructed and then combined into a rectilinear Steiner minimum tree (RSMT). We modify and extend the algorithm to allow obstacles in the routing region. For each routing obstacle, we first introduce four virtual terminals located at its four corners. We then give the definition of FSTs with blockages and prove that they will follow some very simple structures. Based on these observations, a twophase approach is developed for the construction of OARSMTs. In the first phase, we generate a set of FSTs with blockages. In the second phase, the FSTs generated in the first phase are used to construct an OARSMT. Finally, experiments on several benchmarks are conducted. Results show that the proposed method is able to handle problems with hundreds of terminals in the presence of multiple obstacles, generating an optimal solution in a reasonable amount of time.

Optimal Interconnection Trees in the Plane

“…The Geo-Steiner approach has been adopted to the obstacle-avoiding Euclidean Steiner tree problem [433], and to the obstacle-avoiding rectilinear Steiner tree problem [204][205][206]208]. In both cases, problem instances with hundreds of terminals have been solved to optimality.…”

“…As for the minimum spanning tree problem, the separation problem for constraints (5.26) can be solved in polynomial time (in jV j and jEj) by solving a series of minimum cut problems [386,433]. Valid inequalities based on the underlying geometric problem, such as bounds on the degrees of terminals and Steiner vertices, can be added to the formulation [204,433]. Exercises 5.1.…”

Construction of rectilinear Steiner minimum trees with slew constraints over obstacles

“…By applying the lemmas proposed in [10], it can be shown that the trees with the above properties will also follow some simple structures as shown in Fig. 12.…”

“…Therefore, although routing over obstacles is possible, one should be aware of the signal integrity issue and avoid routing long wires on top of obstacles that may lead to complicated post-routing electrical fixups. One way to tackle this problem is to construct an obstacle-avoiding rectilinear Steiner minimum tree (OARSMT) [4][5][6][7][8][9][10]. However, avoiding all obstacles may result in an unnecessary resource overhead.…”

A heuristic for constructing a rectilinear Steiner tree by reusing routing resources over obstacles

“…RSMT has been proven to be an NP-complete problem [1] and has been studied extensively for decades [2,3]. In the last few years, the obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem [4,5], which is a more general and difficult problem than RSMT, has received lots of attention. In practice, several routing layers exist, and most of obstacles commonly occupy the device layer and certain lower metal layers.…”