# 1 Interconnect Layout Optimization by Simultaneous Steiner Tree Construction and Buffer Insertion Presented By Cesare Ferri Takumi Okamoto, Jason Kong.

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1 Interconnect Layout Optimization by Simultaneous Steiner Tree Construction and Buffer Insertion Presented By Cesare Ferri Takumi Okamoto, Jason Kong (ICCAD’96)

2 From the previous Lesson  Buffer insertion and Interconnect Topology optimizations have an important role for Timing optimizations of VLSI circuits.  Previous optimizations algorithms consider independently the 2 problems:  the buffer insertion  Steiner Tree construction (topology optimiz.)

3 Proposed Algorithm  The algorithm (BA-tree) addresses simultaneously the Steiner Tree construction problem and the Buffer insertion problem.  It makes use of two others algorithms:  Heuristic A-tree Algorithm  Van Ginneken algorithm (Buffer insertion)

4 Problem Formulation  Given:  a source S0 and sinks S1..Sn with given positions and RAT associated with each Si  Find:  A Steiner tree Ts that spans S and has buffers inserted  Objective :  Maximized the RAT at the source Source S0 sink1 sink2 sink3 sink4 RAT1

5 Basic Concepts  Steiner Tree:  A tree connecting all terminals as well as other added virtual nodes (Steiner nodes).  Rectilinear Steiner Tree:  Steiner tree such that edges can only run horizontally and vertically.  A-Tree:  Shortest path rectilinear Steiner tree  efficient algorithms can find excellent approximations of the optimal A-tree Steiner tree A-Tree Rectilinear Steiner tree

6 Overall Algorithm  The algorithm consists of 2 phases:  Bottom up tree construction (A-tree alg.)  Top down buffer insertion (Van Ginneken alg.)  The first phase recursively calls the A- tree algorithm

7 First Phase – Recursive Merging  Recursive A-tree creation  Every pair of sub tree roots v and w are evaluated by computing the RAT at the root of of subtree Tr which results from merging of Tv and Tw

8 Second Phase -  Top Down Buffer Insertion (Van Ginneken algorithm )  The option that gives the Maximum Required Arrival Time at root is chosen  Traces back the computation of the first phase that led this option

9 Experimental Results Table: RAT at source (ns) Sequential A-tree, Buffer insertion Proposed alg. 75% bigger RAT than the sequential alg Net with # sinks

10 Conclusions  The BA-tree algorithm was presented, which  derives buffered Steiner tree so that the RAT at the source is Maximized  achieves Steiner tree construction and buffer insertion simultaneously  Experimental Results show that the algorithm increases the timing slack by up 75%  Future Work:  Including the total capacitance minimization and their trade off with the RAT at the source  Incorporating optimal wiresizing for further delay optimizzation

11 optimal wire sizing and buffer insertion for low power nuno alves 7 / december / 2006

12 what’s the paper about? idea is simple: they want to improve delay while take power into account on VLSI circuits. how can we improve delay & routability ? 1.by sizing wires 2.by inserting buffers sizing wires? yes! as we shrink down circuit size, wire becomes a contributor to to signal delay and time. by widening wires we reduce resistance, but we also increase capacitance inserting buffers? yes! read slides from previous class

13 extension from van ginneken this work is an extension from van ginneken work that takes into account: signal slew low power On a circuit, we have the following: length (l), width (w), capacitance (c) and resistance (r) of a wire capacitance and delay of a buffer Model of buffer delay includes slew of the signal

14 algorithm maximizing required arrival time firstly, applies van ginneken algorithm: Algorithm computes the optimal (input capacitance,required arrival time) pairs: For each achievable arrival time, it finds the smallest load achieving it Find optimal buffer configurations. secondly, applies a wire width algorithm from previous tree: 1.Does a similar thing as van ginneken algorithm. It computes the optimal (input capacitance,required arrival time) with different wire widths 2.How much we can scale the wire widths is user specified

15 algorithm to include wire width length (L) C k RAT = T k Load = Ck + (l*w1)*L Load = Ck + (l*w2)*L Load = Ck + (l*w…)*L

16 algorithm to include power consumption Same thing as van ginneken algorithm But we include power as a capacitive value, in addition to (load, required time) pairs

17 experimental results

18 Minimum-Buffered Routing of Non-Critical Nets for Slew Rate and Reliability Control C. Alpert, A. Kahng, B. Liu, I. Mandoiu, A. Zelikovsky Presenter: Elif Alpaslan

19 Motivation Electrical correctness in large interconnects is an important requirement that arises before timing optimization of circuit Elimination of all electrical violations even for non-critical nets is a prerequisite to initiating a meaningful placement and timing optimizations Bounding load capacitance at gate output is a well-known VLSI design methodology to ensure electrical correctness of the nets Bounding the load capacitance at gate output : (+) –improves coupling noise immunity –reduces degradation of signal transition edges –reduces delay uncertainty due to coupling noise –improves reliability with respect to hot-carries oxide breakdown and AC self heating in interconnects –guarantees bounded input rise/fall times at buffers and sinks

20 Minimum-Buffered Routing Problem Given: –Net N with source r and set of sinks S –Binary routing tree T = (r, V, E) for N –Input capacitance c s for each sink s  S –Buffer input capacitance C b –Unit-length wire capacitance C w –Capacitive load upper-bound C U –Buffer-skew bound  Find: buffering of the routing tree T such that –The load cap of each buffer and of the source r is at most C U –The buffer skew is at most  –The number of inserted buffers is minimized

21 Problem Formulation T=(r, V, E) : routing tree for net N T= (r, V, E, B) : buffered routing tree, B is set of buffers located in edges of T For any b in B {r}, the subtree driven by b, is the maximal subtree of D b of T which is rooted at b and has no internal buffers. C w = unit length wire segment capacitance C b = input capacitance of buffer c v = input capacitance of sink or buffer v l e = length of wire segment c e = capacitance of wire segment C u = upper-bound on capacitive load on each buffer Load model: lumped capacitive load model

22 Algorithm 1: Routed Net Buffering Linear Time Greedy Algorithm with a single non-inverting buffer type Definitions used in the algorithm: –Critical Vertex p: a vertex of a routing tree T is critical if p is a bottom- most point of T such that T p can not be driven by a single buffer. –Heaviest Child u of p: u is a heaviest child of p if it accumulates more capacitance than any other child of p.

23 Algorithm 1: Routed Net Buffering Insert buffer on edge (u,p) if C U  c(T u )+c(u,p) Insert buffer at top of heaviest edge if C U > c(T u )+c(u,p)

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