Generation of optimal obstacle-avoiding rectilinear Steiner minimum tree

Abstract

ABSTRACT1 In this paper, we present an efficient method to solve the obstacleavoiding rectilinear Steiner tree problem optimally. Our work is developed based on the GeoSteiner approach, modified and extended to allow rectilinear blockages in the routing region. We extended the proofs on the possible topologies of full Steiner tree (FST) in [4] to allow blockages, where FST is the basic concept used in GeoSteiner. We can now handle hundreds of pins with multiple blockages, generating an optimal solution in a reasonable amount of time. This work serves as a pioneer in providing an optimal solution to this difficult problem.

An exact algorithm for the construction of rectilinear Steiner minimum trees among complex obstacles

“…Note that the definition of FST in this paper is similar to the definitions in [9,10]. However, the obstacles considered in this paper are rectilinear polygons, which are more general and complicated than the rectangles considered in [9,10]. If all obstacles are rectangles, the FSTs defined in this paper degenerate to the ones as defined in [10].…”

“…Otherwise, we can split this FST into smaller FSTs at this virtual terminal. Note that the definition of FST in this paper is similar to the definitions in [9,10]. However, the obstacles considered in this paper are rectilinear polygons, which are more general and complicated than the rectangles considered in [9,10].…”

“…Therefore, virtual terminals are added to simplify their structures in this paper. It should be noted that although virtual terminals are also used in [9,10], there are critical differences when dealing with rectilinear obstacles. In this paper, the virtual terminals are added in such a way that there is at least one virtual terminal on every essential edge of all the obstacles.…”

“…Based on the escape graph, they proposed an algorithm to construct optimal three-terminal and fourterminal OARSMTs. The works presented in [9] and [10] extended GeoSteiner [11] to an obstacle aware version. Their algorithms are able to generate optimal OARSMTs for multi-terminal nets in the presence of rectangular obstacles.…”

Construction of rectilinear Steiner minimum trees with slew constraints over obstacles

“…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.…”