1 L25 : Crosstalk-Concerned Physical Design (2) Jun Dong Cho Sungkyunkwan Univ. Dept. ECE Homepage : vada.skku.ac.kr

2 Min-Crosstalk Top Down Global Routing Algorithm(1) Crosstalk-Critical Region : The region disturbed by crosstalk between two wires Crosstalk generated between random signal net i and j is m = number of crosstalk-critical region crosstalk between two net performed by global routing

3 Min-Crosstalk Top Down Global Routing Algorithm(2) We decide the routing pattern by the position of net that meets design specification. First, whole chip is divided in 4 plane, performs routing by determined routing pattern. Then, performs dividing previous divided plane into 4 plane, and this process performs recursively. Channel Density : the maximum number of wire that passes one channel. : the number of net which connects terminals between and.

4 Min-Crosstalk Top Down Global Routing Algorithm(3) The nodes represents information about routing pattern and channel density of each net. The nodes positioned vertical lines represent different routing pattern of the same net. We define the information of node as follows. Graph contains Routing pattern, Channel density and Information on crosstalk d(degree) : the number of node that is not for random node. The edge represent crosstalk between two nodes, and we consider the crosstalk is 0 when the distance of nets is greater than.

5 Min-Crosstalk Top Down Global Routing Algorithm(4) G = ( V, E ), V = nodes, E = edges; STEP 1 : sorts the crosstalk between node and in ascending order, construct set Z and X. STEP 2 : compute for each net. STEP 3 : choose nodes that has smaller in vertical lines and compute total crosstalk and channel density STEP 4 : Reconstruct graph STEP 5 : Iterate STEP 2 ~ STEP 4 until and are equal. STEP 6 : Choose final result that has minimum crosstalk and meets channel density performed STEP 3.

6 Min-Crosstalk Top Down Global Routing Algorithm(5) Experimental Result

7 An Optimal Track Assignment considering Crosstalk and Power Dissipation Crosstalk cost-function Where is signal sensitivity between net i,j is overlapped length between net i,j is width between net i,j

8 Problem Formulation For Mapping Order for set S T,

9 Previous Approach Track assignment problem is similar to Traveling Salesman Problem(TSP) in general graph algorithm TSP problem is known as NP-Complete. Brute-Force algorithm : Single interval clique : Continuous interval clique(k interval) : Dynamic Programming (greedy approach): In General Cases, Heuristic approach is used. Proposed Algorithm Single interval clique : Find optimal solution in Continuous interval clique: Propose Heuristic algorithm in

10 Special Case I : Containment Interval Clique The shape of Interval Clique Set is Containment : We can find mapping order that has minimum crosstalk in

11 Special Case II : Monotone Interval Clique The shape of Interval Clique Set is Monotone : We can find interval mapping order that has minimum crosstalk in

12 General Case II : Algorithm 3 Theorem : All Interval Set S consists of Containment interval clique set and Monotone interval clique set, so we use below algorithm Step 1 : Clique-Partition ( ) Step 2 : Apply Algorithm1( ) and Algorithm2( ) Step 3 : Merge_Clique ( )

13 The case of Single interval clique Procedure Merge_Clique process is only available as below three process.

14 The case of Single interval clique : In general case Conclusion : Using Algorithm 3, We can find interval mapping order that have minimum crosstalk for Single interval clique in general case. In this case computational complexity is

15 Vertical Crosstalk Crosstalk occurs not only horizontal wires but also occurs vertical wires that exist channel Crosstalk by vertical wires has less size than horizontal wire We can find the LONG-SHORT arrangement order by the method of horizontal wires

16 Example of Single interval clique : Sepcial case Track no. is 4 Using 45 O wire pattern, we can find interval mapping order that has minimum crosstalk for the case that track number is 4.

17 Continuous interval clique We can account track assignment problem in general cases of channel routing as track assignment problem of several numbers of divided sub-channel. We can consider the solution of track assignment problem in general cases of channel routing as Minimization problem of number of LONG-LONG-LONG triple existed in total sub-channel.

18 Continuous interval clique Algorithm 4 [ time ] Step 1 : run wirelength-based left-edge algorithm and Interval clique partitioning [ time] Step 2 : interval type definition (LONG,SHORT)[ time] Step 3 : find maximum LONG-SHORT ordered interval pair by using maximum-edge weight matching [ time] Step 4 : make subchannel that have minimum LONG-LONG- LONG ordered interval triple by using minimum-edge weight matching [

19 Experimental Result : Single interval clique

20 Experimental Result : Continuous interval clique

21 Experimental Result : Deutsch ’ s Difficult Routing Problem

22 References and Suggested Readings [1] Currie M, Sobolewski R, Hsiang TY. High-frequency crosstalk in superconducting microstrip waveguide interconnects. IEEE Transactions on Applied Superconductivity, V.9 N.2 P.3, , 1999 [2] Chou M, White JK. EFFICIENT FORMULATION AND MODEL-ORDER REDUCTION FOR THE TRANSIENT SIMULATION OF THREE-DIMENSIONAL VLSI INTERCONNECT, IEEE Transactions on Computer-Aided Design of Integrated Circuits & Systems, V.16 N.12, , 1997 [3] Vittal A, Mareksadowska M. CROSSTALK REDUCTION FOR VLSI. IEEE Transactions on Computer- Aided Design of Integrated Circuits & Systems, V.16 N.3, , [4] Yen-Tai Lai, Chi-Chou Kao, Wu-Chien Shieh. A Quadratic Programming Method for Interconnection Crosstalk Minimization. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems -, , 1999 [5] Zemo Yang, Samiha Mourad. Deep Submicron On-chip Crosstalk. Proceedings of the 16th IEEE Instrumentation and Measurement Technology, , 1999 [6] Lee, Mankoo. Fringing and coupling interconnect line capacitance model for VLSI on-chip. Proceedings of the IEEE International Symposium on Circuits and Systems, 1996 [7] Hai Zhou and D.F.Wong. Crosstalk-Constrained maze Routing Basd on lagrangian Relaxation. Proceedings of the 1997 IEEE International Conference on Computer Desin : VLSI, 1997 [8] Prashant Saxena, C. L. Liu. Crosstalk Minimization using Wire Perturbation. In Proc. Design Automation Conference, 1999 [9] Hai Zhou, D. F. Wong. Global Routing with Crosstalk Contstraints, In Proc. Design Automation Conference, 1998 [10] Hsiao-Ping Tseng, Louis Scheffer, Carl Sechen, Timing and Crosstalk Driven Area Routing,In Proc. Design Automation Conference, 1999 [11] Tilmann Stohr, Markus Alt, Asmus Hetzel, Jurgen Koehl, Analysis, Reduction and Avoidance of Crosstalk on VLSI Chips, International Symposium on Physical Design, 1998