J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Proc. Int. Symp. Circuits Syst., vol. 1, 1995, pp. 203--206.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a node pair indicates the priority of delay minimization between this pair of nodes. We present an algorithm for the performance driven multiple source routing tree problem based on construction of minimum 8 diameter A trees. Some preliminary results of our work were presented in ISCAS 95 [12]. II. PROBLEM : FORMULA ; TION Given a set of points = A CB D EGF HJILK K K MONQP(R on the Manhattan plane, and a nonnegative weight TVUXWQY[ZO ] as the weight between a each pair of source c d and sink e f to indicate the timing criticality between this pair of points, the ....

J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Pr oc. Int. Symp. Circuits Syst., vol. 1, 1995, pp. 203--206.

....sizing (e.g. 2] 10] 14] After considering the single source case, it is natural to ask what can be done for multi source nets since buses are so prevalent in modern designs and are often a key determinant of system performance. This topic has only recently received attention (e.g. 4] [3], 15] and is the topic of this paper. Our primary contributions are as follows. 1) We propose the Augmented RC Diameter (ARD) as a natural timing metric for multi source optimization. 2) We demonstrate that the ARD can be computed in O(n) time and thus is no harder than computing an ....

J.J. Cong, P.H. Madden, "Performance driven routing with multiple sources," Proc. IEEE Symposium on Circuits and Systems, 1995 pp. 203-6

....Performance driven multi source routing is NP complete [6] even without obstacles. Linear programming has been used to construct lower and upper bounded delay routing trees with a single source, under the linear delay model [12] this work requires an input topology. For multi source routing, [5] heuristically generates minimum cost minimum diameter Steiner arborescences; 4] wiresizes such routing trees via decomposition into source and loading subtrees. None of these algorithms for multiplesource net routing accept path delay bounds as constraints. In the presence of obstacles, Ganley ....

J. Cong, P.H. Madden, "Performance-Driven Routing with Multiple Sources", Proc. IEEE ISCAS, 1995, pp. 203-206

....routing topologies. After considering the various single source formulations, optimization techniques and algorithms, it is natural to ask what can be done in the case of multi source nets since buses are so prevalent in modern designs. This topic has only recently received attention (e.g. 6] [5], 22] and is the topic of this paper. Our primary contributions in this area are as follows. 1) We propose the Augmented RC Diameter (ARD) a natural timing metric based on RC delay models, the arrival times at the inputs (sources) of a multi source and downstream delays from the sinks (outputs) ....

....Tsai, Kao and Cheng proposed a heuristic solution to the repeater insertion problem in which timing requirements were assumed to be given as arbitrary pair wise constraints; their algorithm was based on local optimization and convex programming. Additional work in the multi source domain includes [5] in which Madden and Cong propose an algorithm for constructing low cost minimum diameter rectilinear Steiner trees ( diameter being in the sense of geometric path length rather than RC delay) In [6] Cong and He studied the problem of minimizing a weighted sum of pair wise Elmore delays by wire ....

J.J. Cong, P.H. Madden, " Performance driven routing with multiple sources," Proc. IEEE Symposium on Circuits and Systems, 1995 pp. 203-6

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J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Proc. IEEE Int. Symp. on Circuits and Systems, pp. 1.203-- 1.206, 1995.

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J. Cong and P. H. Madden. Performance driven routing with multiple sources. In Proc. IEEE Int. Symp. on Circuits and Systems, pages 1.203-- 1.206, 1995.

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J. Cong and P. H. Madden. Performance driven routing with multiple sources. In Proc. IEEE Int. Symp. on Circuits and Systems, pages 1.203-- 1.206, 1995.

....in the Manhattan plane very efficiently using a bottom up merging heuristic, and reports sizable delay reduction with only a small wirelength overhead compared to the optimal Steiner tree. The A tree construction method has been extended to signal nets with multiple drivers (as in signal busses) [10]. A graph12 version of the A tree algorithm was also developed [11] which can model routing obstacles and routing congestion in the design. The family of A tree algorithms has been implemented in the TRIO package. Further optimization of interconnect topology involves using more accurate delay ....

J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Proc. IEEE Int. Symp. on Circuits and Systems, pp. 1.203--1.206, 1995.

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J. Cong, and P. H. Madden, "Performance-Driven Routing with Multiple Sources", Proc. IEEE ISCAS, 1995.

.... arborescences outperform traditional heuristic Steiner minimum trees for delay optimization in submicron process technology by up to 66 [10] Alexander and Robins applied the PFA and IDOM algorithms to route timing critical nets in field programmable gate arrays (FPGA s) 1] Cong and Madden [11] proposed a multisource routing algorithm based on constructing minimum cost, minimum diameter arborescences. Exact methods for the MRSA problem can be classified into 1) dynamic programming (DP) 2) integer programming, 3) branch and bound (BNB) enumeration techniques, and 4) mincost max flow ....

J. Cong and P. H. Madden, "Performance driven routing with multiple sources," IEEE Trans. Computer-Aided Design vol. 16, pp. 410--419, Apr. 1997.

....the MRSA problem has received much attention in the field of VLSI computer aided design. Cong et al. 3] showed that, with the current process technology, rectilinear Steiner arborescence has significant advantage over the tradition Steiner tree approach in delay optimization. Cong and Madden [5] proposed a multi source routing algorithm This work was partially supported by the NSF Young Investigator Award MIP 9357582, and a grant from Intel Corporation. KwokShing Leung was with Intel Corporation, Hillsboro, OR 97124, when this work was performed. based on the construction of ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources", Proc. Int'l Symp. on Circuits and Systems, 1995, pp. 1157 -- 1169.

....shortest path tree in the Manhattan plane (also called the A tree) can be constructed very efficiently with sizable delay reduction yet only a small wire length overhead compared to the OST. The A tree construction method has been extended to signal nets with multiple drivers (as in signal busses) [12]. Further optimization of interconnect topology involves using more accurate delay models during routing tree topology construction. For example, the Elmore delay model was used in [2] and the 2 pole delay model was used in [33] to evaluate which node or edge to be added to the routing tree during ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources," Proc. Int'l Symp. on Circuits and Systems, 1995, pp. 1157-- 1169.

....between a node pair indicates the priority of delay minimization between this pair of nodes. We present an algorithm for the performance driven multiple source routing tree problem based on construction of minimum diameter A trees. Some preliminary results of our work were presented in ISCAS 95[12]. 2 Problem Formulation Given a set of points P = fp 1 ; p 2 ; png on the Manhattan plane, and a non negative weight W (p i ; p j ) as the weight between each pair of source p i and sink p j to indicate the timing criticality between this pair of points, the performance driven multiple ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources," Proc. Int'l Symposium on Circuits and Systems, Vol. 1, pp. 203-206, 1995.

....in submicron process technology [3] Okamoto and Cong [13] extended the RSA heuristic to perform simultaneous (arborescence based) topology optimization and buffer insertion. Alexander and Robins [1] used Steiner arborescence in the general graph to route critical nets in FPGA. Cong and Madden [5] proposed a multi source routing algorithm based on constructing minimum cost minimum diameter arborescences. The MRSA problem also has applications in message routing for multicomputer networks [2, 8] In this paper, we present two optimal algorithms for solving the Minimum Rectilinear Steiner ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources", Proc. Int'l Symp. on Circuits and Systems, 1995, pp. 1157 -- 1169.

....design. Cong et al. showed that rectilinear Steiner arborescences outperform traditional heuristic Steiner minimum trees for delay optimization in submicron process technology [5] Alexander and Robins applied the PFA and IDOM algorithms to route timing critical nets in FPGAs [1] Cong and Madden [6] proposed a multi source routing algorithm based on constructing minimum cost minimum diameter arborescences. In this paper we propose three heuristics and two exact algorithms for the MSPSA problem in the following order (2 = exponential time exact algorithm, 4 = polynomial time heuristic) ffl ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources", Proc. Int'l Symp. on Circuits and Systems, 1995, pp. 1157 -- 1169.

....we study the global interconnect sizing and spacing (GISS) problem for delay minimization with consideration of the coupling capacitance, in addition to the area and fringing capacitances. In Section 2, we introduce the problem formulation 1 These nets are multi source nets originally used in [11, 4]. We randomly assign one as the unique single source for each net in our experiments. maximum delay (ns) under different spacings All wires in M1 layer All wires in M5 layer spacing 1 0.5 m random1 random2 1 1.5 m random1 random2 Net1 0.1356 0.3750 0.2386 0.2363 0.1617 0.2890 0.2496 0.2017 ....

J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Proc. IEEE Int. Symp. on Circuits and Systems, pp. 1.203--1.206, 1995.

....for transistor sizing. number of examples for advanced IC technologies. First, we use the STIS algorithm to solve the simultaneous driver and wire sizing (SDWS) problem for multi source nets. 2 These nets are extracted from an Intel high performance microprocessor design and were used in [12, 6] for topology construction and wiresizing optimization. We assume that a chain of cascade drivers is used for each source and the first stage is a minimum size (1x) driver. We compare our STIS method with the CDWS method. The CDWS method uses a constant stage ratio ff = CL=C0 ) 1=N where C0 is ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources," Proc. ISCAS, 1995, pp. 1157--1169.

....tree, we find the intersection of all OEs for the point pairs. There are O(n 2 ) point pairs, resulting in the same number of OEs. It can be shown that the intersection of any number of OEs can be represented by a single OR. A linear time construction of the feasible region is also possible[9]. The shaded OR in Figure 3 shows the feasible region for a minimum diameter A tree center for the given point set. A B C Figure 3: The feasible region for the center of a minimum diameter A tree, the intersection of a number of octilinear ellipses. After construction of the feasible region for a ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources" UCLA Computer Science Department Technical Report #950002, January 1995.

....plane (called the A tree) can be constructed very efficiently using a bottom up merging heuristic with sizable delay reduction yet only a small wire length overhead compared to the OST. The A tree construction method has been extended to signal nets with multiple drivers (as in signal busses) [23]. Further optimization of interconnect topology involves using more accurate delay models during routing tree topology construction. For example, the Elmore delay model was used in [24] and the 2 pole delay model was used in [25] to evaluate which node or edge to be added to the routing tree ....

J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Proc. IEEE Int. Symp. on Circuits and Systems, pp. 1.203-- 1.206, 1995.

....pairs defines the FR for the point set. Figure 16 shows the octilinear ellipses for a set of points, and their intersection which results in the FR. Straight forward computation of the FR takes O(n 2 ) time by intersecting O(n 2 ) OEs; a linear time method to construct the FR was presented in [CoMa95b]. The authors use the A Tree algorithm[CoLZ93] to construct a shortest path tree T from a root point within the FR to the pins of the net. As d T (c; s i ) d(c; s i ) in the A Tree, and c satisfies d(s i ; c) d(c; s j ) D, clearly d T (s i ; c) d T (c; s j ) D for all pairs s i and s j . ....

J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources," Tech. Rep. CSD-950002, UCLA, Jan. 1995.

....The existence of multiple source nets, such as signal busses, complicates interconnect topologyconstruction, as a topologywhich provides good performance for one source may perform poorly for another. An example of such an instance is shown in Figure 15. A method proposed by Cong and Madden[CoMa95] constructs interconnect topologies which limit the maximum path length between any pair of pins to the diameter of the net, while using minimal total wire length. Their Minimum CostMinimum Diameter A Tree (MCMD A Tree) algorithm consists of three main steps: determination of the net diameter, ....

....radius minimization) may be the preferred goal. For the Euclidean metric, Ho et al. HLCW89] presented a method to construct a minimum diameter tree. They determine the smallest enclosing circle for the point set, and then construct a shortest path tree from the center of this circle. The method of [CoMa95] follows a similar approach. For the rectilinear metric, determination of the equivalent of the smallest enclosing circle is simple. A tilted rectangular region (TRR) is defined to be a rectangle with sides having slopes of Sigma1. The rectilinear equivalent of the smallest Euclidean circle, a ....

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J. Cong and P. H. Madden, "Performance Driven Routing with Multiple Sources," Proc. Int'l Symp. on Circuits and Systems, 1995, pp. 1157--1169.

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J. Cong and P. H. Madden, "Performance driven routing with multiple sources," in Proc. Int. Symp. Circuits Syst., vol. 1, 1995, pp. 203--206.

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