Fidducia, C. and R. Rivest, "A greedy channel router", Proceedings 19th Design Automation Conference, 1982, pp. 418-424.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....used is minimized. Complexity: NP hard [LaPa80b] The problem remains NP hard if doglegs are allowed and nets are permitted to contain any number of pins from both sides of the channel [SZYM82a] Several good heuristics for two layer channel routing exist ( DEUT76] YOSH82] MARE82] RIVE81] [FIDD82]) All of these allow doglegs and those of [MARE82] and [RIVE81] permit horizontal and vertical segments to share layers. Lower bounds on the number of tracks needed are developed in [BROW81] Routing in the T shaped and X shaped junctions that result from the intersection of rectangular channels ....

Fidducia, C. and R. Rivest, "A greedy channel router", Proceedings 19th Design Automation Conference, 1982, pp. 418-424.

....a channel routing problem and a possible routing solution is shown in Figure 1. The channel routing problem is NP complete [33] and therefore, there is no known deterministic algorithm to solve it in a polynomial time. Hence, although many different algorithms have been proposed (e.g. 12] 19] [28], 32] 34] the problem of finding the globally optimized solution for channel routing is still open. This article appeared in Evolutionary Computation, Vol. 1, No. 4, pp. 293 311. Cambridge, MA: MIT Press, 1994. E mail: jensl ece.concordia.ca (a) b) Figure 1: An example of a channel ....

....the frequent mutations turn the evolution process into a random walk. On the other hand, reduced mutation probabilities often lead to convergence in a local optimum only. 8 Benchmark System Col. Rows Netlength Vias Yoshimura Yosh. Kuh [34] 12 5 75 21 Kuh Weaver [19] 12 4 67 12 Joo6 13 Greedy [28] 18 8 194 38 Weaver [19] 18 7 169 29 Silk [23] 18 6 171 28 Weaver [19] 11 7 121 21 Burstein s Mighty [32] 13 4 83 8 difficult Packer [12] 12 4 82 10 interactively additional column in the middle of the channel Table 1: Benchmark results. 5.2 Channel routing results The ....

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R. L. Rivest and C. M. Fiduccia, "A Greedy Channel Router," Proc. of the 19th IEEE Design Automation Conference, pp. 418-424, 1982.

....T R depends on the nets that occur in each vertical column which, in turn, depends on the position and orientation of each transistor. Thus, to compute T R , we must determine the nets that must be routed horizontally in each column. This has traditionally been called the channel routing problem [13]. While channel routing considers both horizontal and vertical constraints, cell synthesis methods have generally ignored vertical constraints [11, 9] The fundamental problem is to determine whether a net n requires a track in a column c. We define 0 1 variables net such that net[n, c, r] 1 if ....

R. L. Rivest and C. M. Fiduccia, "A `Greedy' Channel Router," Proc. 19th Design Automation Conf., pp. 120-125, June 1991.

....The approximation methods for multi terminal net CRPs are of the same flavor, but usually more complicated. Both methods are not applicable to real world problems because of their terrible approximation factors. But the algorithm from [185] is at least compatible with the greedy strategy from [153], which seems to work well in practice. The reason is, that the interblock routing method used is similar to the procedure of the greedy strategy, which is a kind of right pushing algorithm as the algorithm in [124] for knock knee routing. The greedy router scans the channel from left to right ....

R. L. Rivest and C. M. Fiduccia. A greedy channel router. In Proceedings of the 19th Design Automation Conference DAC'82, pages 418--424, 1982.

....for interconnections. Extensive studies have been carried out on the conventional channel routing problem, and there are several channel routers which can produce solutions that use at most one or two tracks beyond the channel density for most of the practical test examples. For example, see [6, 22, 18, 2, 16]. To further reduce the channel routing area, several channel routers have been designed to take advantage of the possibility of utilizing the routing area over the cells for interconnections [7, 13, 19, 12] These routers are called over the cell channel routers. In most cases, over the cell ....

....problem of finding a minimum density spanning forest of a graph. We demonstrate that the minimum density spanning forest problem is NP hard. We also present an efficient heuristic algorithm which produces very satisfactory results. Based on these algorithms together with a greedy channel router [18] for the third step, we design an efficient over the cell channel router which performs very well for all test examples. On the average, our routing solution attains a saving of 19.6 of the channel routing area when compared with the optimal two layer channel routing solutions, and attains a ....

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R. L. Rivest and C. M. Fiduccia. "A 'Greedy' Channel Router," Proc. 19th Design Automation Conf., pp. 418-424, 1982.

....also give a new theoretical upper bound # d 2 # 2 for arbitrary four layer channel routing problems. 1. Introduction A key problem in VLSI layout design and implementation is the channel routing problem. The two layer channel routing problem has been studied extensively in the past ten years [9, 21, 22, 4, 20]. There are several two layer channel routers which can produce channel routing solutions using at most 1 or 2 tracks more than channel density for most practical problems. With the advance in VLSI technology, utilization of more than two layers for signal routing has become feasible. As mentioned ....

R. L. Rivest and C. M. Fiduccia. "A 'Greedy' Channel Router," Proc. 19th Design Automation Conf., pp. 418-424, 1982.

....ancestors in the vertical constraint graph during net selection. Enforcing vertical constraints during track assignment may generate routes that require more tracks than are necessary. 20 3.2. 2 Greedy Channel Router In 1982 Rivest and Fiduccia described their greedy channel router [RF82] They presented a column oriented method of routing two layer gridded channels. Their basic idea was to start at the left edge of the channel and completely wire each column before moving on to the next in order to avoid the creation of VCVs. Their algorithm specifies that connections in a ....

Ronald L. Rivest and Charles M. Fiduccia. A `greedy' channel router. In Proc. 19th ACM/IEEE Design Automation Conference, pages 418--424, 1982.

....area is used for channel routing. The two layer grid based channel routing problem has been well formulated and studied extensively. There are several grid based channel routers which can consistently produce channel routing solutions which are at most one or two tracks within optimal solutions [De76, YoKu82, RiFi82, BuPe83, ReSS85]. A further study [De85] showed that the routing solutions of these grid based router could be compacted to obtain a 15 20 area reduction. Both straight track compaction [De85, WoLi86, Ch86] and contour routing compaction [De85, XiKu87, Ro87, ChDe88] have been investigated. Usually these ....

.... grant MIP 87 03273, by the Semiconductor Research ####################################################### Based solution # of tracks channel height after compaction ####################################################### [De76] 21 49.0 ####################################################### [RiFi82] 20 48.0 ####################################################### [YoKu82] 20 47.0 ####################################################### [ReSS85] 19 47.0 ####################################################### [BuPe83] 19 46.0 ####################################################### [Ro87] 81 ....

Rivest, R. L. and C. M. Fiduccia, "A 'Greedy' Channel Router". Proc. 19th Design Automation Conf. (1982) pp. 418-424.

....modified vertical constraint graph. Their results demonstrated a large improvement over the Dogleg and Left Edge Algorithms, especially in the minimum number of tracks required and overall processing time. Around the same time, another heuristic based router was developed by Rivest and Fidducia [6] called the greedy channel router. This router applies the same principles as the Left Edge and Dogleg routers do; however, the channel is scanned on a column by column basis instead of track by track methods of the former. Unrestricted doglegging is allowed; however, it may be necessary to add ....

R. L. Rivest and C. M. Fiduccia, "A Greedy Channel Router," Proc. 19th Design Automat. Conf., pp. 418-424, June 1982.

....of the system by providing routing flexibility and supporting features needed to handle a wide range of design styles in generating CMOS custom cells. 1 Introduction Automatic custom cell synthesis presents some unique constraints to the routing problem not present in simple channel routing [1] [2] and switchbox routing models [3] 4] The boundary of the routing problem need not necessarily be rectangular. It can have an arbitrary rectilinear shape. In this general problem, pins are not restricted to the boundaries (as is the case in channel and switchbox routers) They can be located ....

....and non uniform grid schemes is shown in Figure 10. In the next section an algorithm for obtaining the denser virtual grid from the technology information is presented. Figure 8. Track overlapping graph for uniform grid with Metal2 spacing. 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 path[1] path[2] path[3] path[4] path[5] path[6] path[7] metal2 metal1 polysilicon grid line capacity 3 3 3 3 3 3 3 Figure 9. Track overlapping graph for non uniform grid with polysilicon spacing 1 1 1 2 2 2 3 3 3 4 4 4 5 5 6 6 5 7 7 path[1] path[2] path[3] path[4] path[5] path[6] path[8] metal2 metal1 ....

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TR. L. Rivest and C. M. Fiduccia, "A Greedy Channel Router," Proc. 19th Design Automation Conference, 1982, 418-424.

....the upper and one on the lower boundary of the grid. These have to be connected. A solution (layout) is given by edge disjoint paths (wires) that connect corresponding terminals within the channel. There are essentially two different routing models, knock knee [2] 10] and [12] and Manhattan [1] [11] and [13] In this paper we consider the knock knee model, where two wires may cross or both bend at a vertex, i.e. form a knock knee. In Manhattan routing knock knees are not allowed. Now, to avoid physical contacts between different wires, the edges of the paths are assigned to different ....

R.L. Rivest, C.M. Fiduccia. A greedy channel router. Proc. 19th Design Automation Conference (1982) 418-424

....utilizing two routing layers in the channels for interconnections. Conventional channel routing has been extensively studied, and there are several channel routers which can produce solutions using at most one or two tracks more than channel density for most practical problems. For example, see [7, 23, 20, 1, 19]) To further reduce the channel routing area, some channel routers use the extra routing area over the cells for interconnections [9, 15, 21, 14, 3, 5] These routers are called over the cell channel routers. 9] presents an algorithm that produces single layer planar routing over the cells for ....

Rivest, R. L. and C. M. Fiduccia, "A 'Greedy' Channel Router". Proc. 19th Design Automation Conf. (1982) pp. 418-424.

....example. A new lower bound algorithm LB2 is presented in Section 3, and a tighter lower bound algorithm LB3 is presented in Section 4. Experimental results are detailed in Section 5, and conclusions are drawn in Section 6. 2 RELATED WORK The channel routing problem has been studied extensively [9, 13, 15, 16, 17, 18, 19, 21, 22, 23, 25, 27, 28, 29]. However, most previous work has focussed on finding a routing, and little work has been done on finding a tighter lower bound for CRPs. In recent years, several branch and bound type algorithms have been proposed to find optimal solutions [19, 27] These algorithms require maintaining a search ....

R. L. Rivest and C. M. Fiduccia. A greedy channel router. In 19th Design Automation Conference, 1981.

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R. L. Rivest and C. M. Fiduccia, "A greedy channel router", Proc. 19th Design automation conference, pp. 418 - 424 (1982).

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