A Min-area Solution to Performance and RLC Crosstalk Driven Global Routing Problem Tong Jing, Ling Zhang, Jinghong Liang Jingyu Xu, Xianlong Hong Jinjun Xiong, Lei He CS&T Department EE Department Tsinghua University UCLA Beijing 100084, China Los Angeles, CA, USA Speaker: Jinghong Liang

ASP-DAC2005, Shanghai, China Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions November 27, 2018 ASP-DAC2005, Shanghai, China

Backgrounds VLSI / ULSI Coupling effects and crosstalk System-On-a-Chip (SOC) Clock frequency increases New challenge to global routing Global routing plays an important role in very/ultra large scale integrated circuits (VLSI/ULSI) physical design The progress in VLSI/ULSI enables system-on-a-chip (SOC) integration instead of system-on-a-board (SOB) integration Chip design is with greatly shrinking of geometries and giga-hertz clock frequencies All these advances enable us to get high-performance chips However, one of the great concerns is coupling effects and crosstalk Crosstalk elimination has become a challenge to global routing November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Previous Work (1) The existing works can be divided into three categories Noise modeling [T. Sakurai, S. Kobayashi, and M. Node. ISCAS, 1991] Derived expressions for a coupling capacitance and a crosstalk voltage height [L. He and K. M. Lepak. ISPD, 2000] Declared that on-chip inductance, especially mutual inductance, should be considered for high-performance interconnect design and presented the effective coupling model, called the Keff model November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Previous Work (2) Noise minimization [T. X. Xue, E. S. Kuh. IEEE Trans on CAD, 1997] Described a two-pass algorithm including region-based crosstalk risk estimation and crosstalk reduction [H. Zhou and D. F. Wong. IEEE Trans on CAD, 1999 ] Presented a cost function taking crosstalk into consideration, and is used during the phase of constructing the routing tree [J. J. Xiong and L. He. IEEE Trans on CAD, 2004] Proposed a three-phase algorithm based on crosstalk budgeting, simultaneous shield insertion and net ordering (SINO), and local refinement November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Previous Work (3) Simultaneous noise minimization and performance optimization [L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ASICON, 2003]----(PO-GR) [J. Y. Xu, X. L. Hong, T. Jing, L. Zhang, J. Gu. ASP-DAC, 2004] Both proposed performance optimization global routing algorithms considering crosstalk reduction. The former mainly focuses on coupling capacitance and uses spacing method. The latter considers coupling inductance and is based on shield insertion [L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ISCAS, 2004]----(T-PO-GR) Presented an efficient RLC crosstalk reduction algorithm November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions November 27, 2018 ASP-DAC2005, Shanghai, China

Global Routing Problem With the progress in multi-layer routing technology, routing area is a whole chip plane A net can be specified as a set of nodes in global routing graph (GRG) The problem of routing a net can be described as a rectilinear Steiner minimal tree (RSMT) problem of specified nodes in GRG. November 27, 2018 ASP-DAC2005, Shanghai, China

Global Routing Graph (GRG) 1 GRC GRG e v 2 1 v November 27, 2018 ASP-DAC2005, Shanghai, China

LSK Model for RLC Crosstalk Estimation 1 K f(i) g(j) gl Ni Nj gr Wire order Kij Fast computation of Ki,j: The total amount of inductive coupling induced on Nit: For all net segments Njt that are sensitive to Nit Different from earlier noise model Sakurai, the LSK model considers coupling inductance between adjacent and non-adjacent sensitive nets November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Tabu Search The basic idea of this technology is simple, which records and taboos the local minimum points that have been reached so as to avoid getting stuck at these points and finds out new search ways that could lead to the global minimum point eventually. Select an initial solution xnow, and set Tabu list H = empty; While not meet the stop conditions do Generate a candidate list from the neighborhood of xnow that does not conflict with H; Select the best solution xnext from the candidate list; xnow = xnext; Update Tabu list H; End While There are 3 key factors in Tabu search: tabu object, tabu length, and aspiration rule November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions November 27, 2018 ASP-DAC2005, Shanghai, China

Our Main Contributions Goal: Reduce the final routing area by means of improving the gross algorithm based on holistic optimization The main contribution of this paper is a min- area solution to performance and RLC crosstalk driven global routing problem The proposed algorithm can achieve smaller routing area and fewer shields under the same design constraints, yet use less running time November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Problem Formulation Let Then we have Minimize Subject to: (1) (2) (3) Formula(1) is the congestion constraint, which forbids the overflow on each GRG edge Formula(2) guarantees the actual delay value from source i to sink j, T(i, j), is no more than the given timing constraint TD (i, j) Formula(3) sets the upper bound of LSK, , for each source sink pair ij. November 27, 2018 ASP-DAC2005, Shanghai, China

The Main Flow of AT-PO-GR Use Grrandom() to get an initial solution X0 It considers congestion and timing issues Use CtkEst() to budget and estimate crosstalk in X0 Iterate Grrandom(X0) to rip-up X0 so as to reduce its crosstalk, and get a good mid-solution Xtemp Use Gr(Xtemp) to reduce wire length, congestion, and delay Get a solution X1 Use CtkEli() to eliminate crosstalk in X1 by means of shield insertion and changing net orders Get the final result X2 November 27, 2018 ASP-DAC2005, Shanghai, China

Use Grrandom() to get an initial solution X0 A new cost formula of GRG edge taking crosstalk into account is used as follows , (4) where ct is the capacity of edge t, ft is the number of used tracks in edge t, δ is a small real number that validates formula (4) while ct is 0, is the actual congestion of edge t, K is a large integer used as the penalty factor, wt is the weighted cost of edge t, and nvt is the number of net segments in edge t that violate crosstalk constraint. Considering possible shield may be inserted due to these net segments, we add nvt in such that these edges tend to become more congested. Then, nets crossing such edges will have higher cost and thus it will be avoided. November 27, 2018 ASP-DAC2005, Shanghai, China

Use CtkEst() to budget and estimate crosstalk in X0 Firstly, Where is the crosstalk bound at sink pij for net Nj len is the total length from the source pio to sink pij. Secondly, having got , CtkEst() computes actual Kit with LSK model. At last, we can obtain Kslack for each source-sink pair ij. Kslack has the following definition. November 27, 2018 ASP-DAC2005, Shanghai, China

Use Gr(Xtemp) to get a solution X1 Transition from a local minimum point Gr() include 3 different strategies: stochastic optimization, deterministic optimization, and local enumeration optimization strategy. Grrandom() only uses stochastic optimization strategy. November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Use CtkEli() to eliminate crosstalk in X1 by means of shield insertion and changing net orders Firstly, insert shields in each GRG region so that the crosstalk of most regions is within the given bound Secondly, insert shield in those regions which have possible remnant crosstalk, so that crosstalk is completely eliminated Finally, delete unnecessary shields so that the final area is minimized November 27, 2018 ASP-DAC2005, Shanghai, China

Pseudo code of AT-PO-GR November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions November 27, 2018 ASP-DAC2005, Shanghai, China

Experimental Environments Platform Hardware: sun V880 fire workstation Software: gcc2.9.1, solaris5.8 Benchmark Data Circuits Number of nets GRG grids C2 745 9*11 C5 1764 16*18 C7 2356 avq 21581 65*67 Parameters Setting LSK bound at each sink is set to be 1000 Na=350, Nb=20, Nc=10, and Tabu length=3 November 27, 2018 ASP-DAC2005, Shanghai, China

In Comparison with Typical Algorithms (1) PO-GR [L. Zhang, T. Jing, X. L. Hong, 2003] is the first algorithm to study inductance coupling noise, timing performance and routability simultaneously at global routing level. It uses SA algorithm in its crosstalk elimination. (2) T-PO-GR [L. Zhang, T. Jing, X. L. Hong, 2004] runs much faster than PO-GR with the similar routing results. But the routing area and shield number in T-PO-GR are comparably larger than those in PO-GR We will compare our AT-PO-GR with the above algorithms focusing on area, running time, etc. November 27, 2018 ASP-DAC2005, Shanghai, China

The comparison of wire length, running time, and routing area between AT-PO-GR and PO-GR Circuit C2 C5 C7 avq AT-PO-GR Vionum (X0) 654 1600 1960 9885 Vionum (Xtmp) 608 1485 1902 9690 Decrease 5.66% 7.19% 2.96% 1.97% Vionum (X1) 622 1522 Wire length (X0) 477516 1415238 1588218 10154788 Wire length (X1) 450730 1266044 1530654 9906136 Running time (s) 84.33 245.55 336.94 6277.5 Area 150187 269304 337378 1206×986 PO-GR Wire length 471840 1327942 1606928 -- 2457.39 5738.45 9985.52 160190 269309 364366 The decrease of AT-PO-GR running time compared with PO-GR running time 3.43% 4.28% 3.37% The decrease of AT-PO-GR wire length compared with PO-GR wire length 4.47% 4.66% 4.75% The decrease of AT-PO-GR area compared with PO-GR area 7.73% 1.62% 4.38% November 27, 2018 ASP-DAC2005, Shanghai, China

The comparison of wire length, running time, and routing area between AT-PO-GR and T-PO-GR Circuit C2 C5 C7 avq AT-PO-GR Running time (s) 84.33 245.55 336.94 6277.5 Area 150187 269304 337378 1206×986 Shield numbers 166 484 665 4131 Wire length 450730 1266044 1530654 9906136 T-PO-GR 2457.39 5738.45 9985.52 -- 160190 269309 364366 204 527 684 471840 1327942 1606928 The decrease of AT-PO-GR running time / T-PO-GR running time 50.12% 42.25% 46.58% The decrease of AT-PO-GR wire length compared with T-PO-GR wire length 2.10% 3.25% 5.29% The decrease of AT-PO-GR area compared with T-PO-GR area 21.34% 12.74% 6.67% The decrease of AT-PO-GR shield numbers compared with T-PO-GR shield numbers 18.63% 8.16% 2.78% November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Discussions Grrandom() can reduce crosstalk violation number（2%-7% ） The runtime of AT-PO-GR is no more than 5% of that of PO-GR AT-PO-GR can reduce wire length by more than 4% compared with PO-GR Running time of AT-PO-GR is about half of that of T-PO-GR The wire length of AT-PO-GR is shorter than that of T-PO-GR AT-PO-GR also gets improvements in area and shield number compared with T-PO-GR November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Outline 1. Introduction 2. Preliminaries 3. Our Work (AT-PO-GR Algorithm) 4. Experimental Results & Discussions 5. Conclusions November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Conclusions A min-area solution to performance and RLC crosstalk driven global routing problem has been presented in this paper The experimental results have shown that this algorithm is able to: (i) obtain routing solutions with less routing area compared with typical existing works (ii) preserve good routing results and greatly decrease running time compared with typical existing works November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Future Work As our future work, we plan to find more specific methods to construct the Steiner tree set for crosstalk minimization, and better strategies for crosstalk budgeting November 27, 2018 ASP-DAC2005, Shanghai, China

ASP-DAC2005, Shanghai, China Thank you! Jinghong Liang(梁敬弘) Dept . of CST, Tsinghua Univ. Beijing 100084, P. R. China Tel.: +86-10-62785428 Fax: +86-10-62781489 E-mail: liangjh03@mails.tsinghua.edu.cn November 27, 2018 ASP-DAC2005, Shanghai, China