On Finding a Staircase Channel With Minimum Crossing Nets in a Vlsi Floorplan

Abstract

A VLSI chip is fabricated by integrating several rectangular circuit blocks on a 2D silicon floor. The circuit blocks are assumed to be placed isothetically and the netlist attached to each block is given. For wire routing, the terminals belonging to the same net are to be electrically interconnected using conducting paths. A staircase channel is an empty polygonal region on the silicon floor bounded by two monotonically increasing (or decreasing) staircase paths from one corner of the floor to its diagonally opposite corner. The staircase paths are defined by the boundaries of the blocks. In this paper, the problem of determining a monotone staircase channel on the floorplan is considered such that the number of distinct nets whose terminals lie on both sides of the channel, is minimized. Two polynomial-time algorithms are presented based on the network flow paradigm. First, the simple two-terminal net model is considered, i.e., each net is assumed to connect exactly two blocks, for which an O(n×k) time algorithm is proposed, where n and k are respectively the number of blocks and nets on the floor. Next, the algorithm is extended to the more realistic case of multi-terminal net problem. The time complexity of the latter algorithm is O((n+k)×T), where T is the total number of terminals attached to all nets in the floorplan. Solutions to these problems are useful in modeling the repeater block placement that arises in interconnect-driven floorplanning for deep-submicron VLSI physical design. It is also an important problem in context to the classical global routing, where channels are used as routing space on silicon.

Hierarchical partitioning of VLSI floorplans by staircases

“…Given F and its netlist, the following problems on ms-cuts may be formulated: -Min-cut Problem P c [Majumder et al 2004]: an ms-cut with minimum cut-size; -Number-balance Problem P n [Dasgupta et al 2002]: an ms-cut maximizing the number-balance ratio, min (n l ,n r ) max (n l ,n r ) ; -Area-balance Problem P A : an ms-cut maximizing the area-balance ratio…”

“…An instance of P Ac with unit area blocks is equivalent to an instance of P nc . As we require a balanced ms-cut, we construct a graph, similar to that for problem P c [Majumder et al 2004], and we apply a maxflow-based balanced bipartitioning method [Yang and Wong 1996].…”

“…This partitions the set of blocks in F into two parts, namely, left-set and right-set, respectively. A mincost staircase cut (MSC) is a staircase such that the number of distinct nets attached to the blocks on both the left-set and right-set, is minimum [Majumder et al 2004]. Monotone staircases, henceforth referred as ms-cuts of a floorplan F , have been shown to be particularly advantageous to efficient routing [Guruswamy and Wong 1988;Sur-Kolay and Bhattacharya 1991;Majumder et al 2004].…”

“…A maxflow-based algorithm [Majumder et al 2004] can determine in polynomial time a series of ms-cuts with minimum number of crossing nets, that is, distinct nets with terminals on either side. These ms-cuts recursively bipartition a given rectangular floorplan until degenerate staircases, that is, straight cutlines are obtained.…”

“…This in turn, saves routing area. More often than not, the above algorithm [Majumder et al 2004] yields an unbalanced tree, which may reduce the efficacy of the scheme. In general, a balanced physical hierarchy [Chang et al 2003] is preferable for reducing overall time complexity and congestion.…”