A Length Matching Routing Algorithm for Set-Pair Routing Problem

Abstract

In the routing design of interposer and etc., the combination of a pin pair to be connected by wire is often flexible, and the reductions of the total wire length and the length difference are pursued to keep the circuit performance. Even though the total wire length can be minimized by finding a minimum cost maximum flow in set pair routing problems, the length difference is often large, and the reduction of it is not easy. In this paper, an algorithm that reduces the length difference while keeping the total wire length small is proposed. In the proposed algorithm, an initial routing first obtained by a minimum cost maximum flow. Then it is modified to reduce the maximum length while keeping the minimum total wire length, and a connection of the minimum length is detoured to reduce the length difference. The effectiveness of the proposed algorithm is confirmed by experiments.

A Fast Length Matching Routing Pattern Generation Method for Set-Pair Routing Problem Using Selective Pin-Pair Connections

“…In the set-pair routing, a routing pattern is said to be feasible if each wire connects sourcepin and sink-pin without using grid intersections of obsta- cles. The existence of a feasible routing pattern is easily checked by a maximum flow algorithm [6]. Therefore, in the following discussion, we focus on the problem instances that have a feasible routing pattern.…”

“…In order to obtain a routing pattern that achieves length matching as much as possible in a set-pair routing problem, a heuristic algorithm is proposed [6] (Hereinafter, called Nakatani algorithm). This algorithm tries to find a length matching routing pattern while keeping the total wire length small.…”

“…In order to obtain a routing pattern by a network flow algorithm, pins and routing area are converted to a flow graph and a primary source that is connected to all sourcepins and a primary sink that is connected to all sink-pins are added to the graph, then a maximum flow from the primary source to the primary sink is used as routing paths [6]. We define the degree of overlapping bounding boxes for each edge of a routing area as the number of overlapping bounding boxes on each edge, in which the target pin-pairs of them are not connected yet (Hereinafter, it is simply called the overlapping degree).…”

“…In the routing design such as silicon interposer [1], [2], printed circuit board (PCB) [3], [4], FPGA [5] and etc., the combination of a pin-pair to be connected by a wire is often flexible. The set-pair routing problem [6] is defined for modeling such routing designs, in which a connection requirement is set between a source-pin set and a sink-pin set. In this routing problem, a length matching routing pattern while keeping wire lengths small is often required under the assumption of signal propagation delay is proportional to the wire length.…”

“…routing problem has been proposed [6] (Hereinafter, it is called the Nakatani algorithm). This algorithm generates a length matching routing pattern while keeping the total length as small as possible by improving an initial solution.…”