add CSS content

luk036 · luk036 · commit 7315360625f8 · 2025-04-30T15:46:49.000+08:00
diff --git a/algo4dfm/css_under_pv.html b/algo4dfm/css_under_pv.html
@@ -2,7 +2,7 @@
 <html>
   <head>
     <title>
-      ⏰ Clock Skew Scheduling Under Process Variations
+      ⌚ Clock Skew Scheduling Under Process Variations
     </title>
     <meta charset="utf-8" />
     <meta
@@ -29,11 +29,11 @@
 count: false
 class: nord-dark, middle, center
 
-# ⏰ Yield-driven Clock Skew Scheduling Under Process Variations
+# ⌚ Yield-driven Clock Skew Scheduling Under Process Variations
 
 @luk036
 
-2025-04-26
+2025-04-30
 
 ---
 
@@ -50,11 +50,9 @@
 
 ## 📝 Abstract (II)
 
-.font-sm.mb-xs[
 The lecture goes on to discuss primitive solutions and their shortcomings, such as pre-allocating timing margins and using the Least Center Error Square (LCES) problem formulation. The lecture also introduces more advanced techniques such as slack maximization (EVEN) and prop-based methods that distribute slack along the most timing-critical cycle based on Gaussian models. The drawbacks of these methods are highlighted, particularly their assumptions about gate delay distributions.
 
 Finally, statistical static timing analysis (SSTA) and the use of statistical methods to account for process variations are discussed. The concept of the most critical cycle is introduced, and the lecture provides experimental results to demonstrate the effectiveness of various clock skew scheduling techniques.
-]
 
 ---
 
@@ -66,9 +64,9 @@
 
 -   Problem formulation
 
--   Traditional clock skew scheduling ⏰
+-   Traditional clock skew scheduling
 
--   Yield-driven clock skew scheduling ⏰
+-   Yield-driven clock skew scheduling
 
 -   Minimum cost-to-time ratio cycle formulation
 
@@ -128,7 +126,7 @@
 
 ---
 
-## Zero skew vs. Useful skew
+## Zero Skew vs. Useful Skew
 
 -   Zero skew ($t_i = t_f$) : Relatively easy to implement.
 
@@ -202,8 +200,6 @@
 
 ## Basic Bellman-Ford Algorithm
 
-.font-sm.mb-xs[
-
 ```matlab
 function BellmanFord(list vertices, list edges, vertex source)
     // Step 1: initialize graph
@@ -225,7 +221,6 @@
             error "Graph contains a negative-weight cycle"
 return u[], predecessor[]
 ```
-]
 
 ---
 
@@ -262,8 +257,7 @@
 
 -   However, many skew values are on the bounds of feasible range.
 
-![Timing uncertainty emerges under process
-variations](lec05.files/fig07.png)
+    ![Timing uncertainty emerges under processvariations](lec05.files/fig07.png)
 
 ---
 
@@ -349,8 +343,7 @@
         Tolerant to Process Variations", DAC'96)
 
 -   Quadratic Programming method
-    -   (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⏰ for
-        improved reliability via quadratic programming", ICCAD'99)
+    -   (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling for improved reliability via quadratic programming", ICCAD'99)
 
 Shortcoming: might reduce some slacks to be zero to minimum **total** CES.
 This is not optimal for yield.
@@ -360,8 +353,7 @@
 ## Primitive solution (3)
 
 -   Incremental Slack Distribution
-    -   (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⏰
-        under process variations", ISQED'06)
+    -   (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling under process variations", ISQED'06)
 
 -   Advantage: check all skew constraints
 
@@ -656,25 +648,18 @@
 
 ## Slack Maximization (C-PROP)
 
--   Slack Maximization Scheduling $$\begin{array}{ll}
-        \text{maximize} & {\color{orange}\beta} \\
-        \text{subject to} & {\color{red}t_j} - {\color{red}t_i} \leq \mu_{ij} - \sigma_{ij} {\color{orange}\beta}
-    \end{array}$$
+-   Slack Maximization Scheduling
+  $$\begin{array}{ll}
+    \text{maximize} & {\color{orange}\beta} \\
+    \text{subject to} & {\color{red}t_j} - {\color{red}t_i}\leq \mu_{ij} - \sigma_{ij} {\color{orange}\beta}
+  \end{array}$$
 
 -   Equivalent to the *minimum cost-to-time ratio cycle* problem (MMC), where:
     -   ${\color{orange}\beta}^* = \frac{\sum_{(i,j)\in C} \mu_{ij} }{\sum_{(i,j)\in C} \sigma_{ij} }$
     -   $C$: critical cycle (first negative cycle)
 
 ---
 
-## Probability Observation
-
--   Prob(timing failure) turns out to be an Error function that solely
-    depends on this ratio. Therefore, it is justified to use this ratio
-    as critical criteria.
-
----
-
 ## Whole flow
 
 -   After determining the clock arrival time at each vertex in the most
@@ -703,8 +688,6 @@
 
 ## Advantages of This Method
 
--   Justified by probability observation.
-
 -   Fast algorithm exists for minimum cost-to-time ratio cycle problem.
 
 -   Reduce to Even when all variances are equal.
@@ -752,8 +735,7 @@
     Any monotonic decreasing function will do.
 
 -   Theorem: if $g(\beta)$ and $f_{ij}(\beta)$ are *monotonic decreasing*
-    functions for all $i$ and $j$, then there is a unique solution to the problem.
-    (prove later).
+    functions for all $i$ and $j$, then there is a unique solution to the problem. prove later).
 
 -   Question 1: Does this generalization have any application?
 
@@ -1076,6 +1058,18 @@
 
 ---
 
+## Conclusion and Future Direction
+
+- Asymmetric Delays
+
+Path delays often exhibit asymmetric and heavy-tailed distributions, which cannot be accurately captured by the commonly used Gaussian model.
+
+- GEV Distribution
+
+The Generalized Extreme Value (GEV) distribution can better fit the actual delay distributions, with its flexible parameters allowing for a variety of skewness and tail behaviors.
+
+---
+
 count: false
 class: nord-dark, middle, center
 
diff --git a/algo4dfm/lec05.md b/algo4dfm/lec05.md
@@ -1,4 +1,4 @@
-# Lecture 05a - ⏰ Clock Skew Scheduling Under Process Variations
+# Lecture 05a - ⌚ Clock Skew Scheduling Under Process Variations
 
 @luk036
 
@@ -15,7 +15,7 @@
 - Useful skew design 有效偏差设计
   - Critical cycles 关键环
   - Negative cycles 负环
-- Clock skew scheduling ⏰ (CSS) 时钟偏差安排/规划
+- Clock skew scheduling ⌚ (CSS) 时钟偏差安排/规划
 - Yield-driven CSS 产品率驱动时钟偏差安排
 
 ## 🗺️ Overview
@@ -24,9 +24,9 @@
 
 - Problem formulation
 
-- Traditional clock skew scheduling ⏰
+- Traditional clock skew scheduling ⌚
 
-- Yield-driven clock skew scheduling ⏰
+- Yield-driven clock skew scheduling ⌚
 
 - Minimum cost-to-time ratio cycle formulation
 
@@ -255,7 +255,7 @@ variations](lec05.files/fig07.png)
   - (J. L. Neves and E. G. Friedman, "Optimal Clock Skew Scheduling
     Tolerant to Process Variations", DAC'96)
 - Quadratic Programming method
-  - (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⏰ for
+  - (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⌚ for
     improved reliability via quadratic programming", ICCAD'99)
 
 Shortcoming: might reduce some slacks to be zero to minimum **total** CES.
@@ -264,7 +264,7 @@ This is not optimal for yield.
 ## Primitive solution (3)
 
 - Incremental Slack Distribution
-  - (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⏰
+  - (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⌚
     under process variations", ISQED'06)
 - Advantage: check all skew constraints
 
@@ -510,7 +510,7 @@ Final result: $T_1=T_1+T_{s_1}+T_{s_3}$
   K. Saluja, "Yield-Driven, False-Path-Aware Clock Skew Scheduling",
   IEEE Design & Test of Computers, May-June 2005
 
-# Lecture 05b - ⏰ Clock Skew Scheduling Under Process Variations (2)
+# Lecture 05b - ⌚ Clock Skew Scheduling Under Process Variations (2)
 
 ## 🗺️ Overview
 
@@ -748,7 +748,7 @@ Final result: $T_1=T_1+T_{s_1}+T_{s_3}$
 
 ![image](http://www.plantuml.com/plantuml/svg/TOx13i8W44Jl_Ogv0MhKUAJfgLz208L6CB7RMAF-kniCnXxSsqnstem6GNUGb6B66fJChB33eMrm2_7i8VC5sP-si7VBSihENq6g0Pz6YN6Uschye_di2l3BDR_OleBXvpZIMFd7c1r8O9ni00L3nGVhz91nCoXmKOydFmwIX7gXmtwnXSIYdDtLP_0R)]
 
-# ⏰ Clock Skew Scheduling for Unimodal Distributed Delay Models
+# ⌚ Clock Skew Scheduling for Unimodal Distributed Delay Models
 
 @luk036
 
diff --git a/algo4dfm/lec05a-remark.html b/algo4dfm/lec05a-remark.html
@@ -2,7 +2,7 @@
 <html>
   <head>
     <title>
-      Lecture 05a - ⏰ Clock Skew Scheduling Under Process Variations
+      Lecture 05a - ⌚ Clock Skew Scheduling Under Process Variations
     </title>
     <meta charset="utf-8" />
     <meta
@@ -29,7 +29,7 @@
 count: false
 class: nord-dark, middle, center
 
-Lecture 05a - ⏰ Clock Skew Scheduling Under Process Variations
+Lecture 05a - ⌚ Clock Skew Scheduling Under Process Variations
 ============================================================
 
 @luk036
@@ -74,7 +74,7 @@
 -   Useful skew design 有效偏差设计
     -   Critical cycles 关键环
     -   Negative cycles 负环
--   Clock skew scheduling ⏰ (CSS) 时钟偏差安排/规划
+-   Clock skew scheduling ⌚ (CSS) 时钟偏差安排/规划
 
 ]
 .pull-right[
@@ -92,9 +92,9 @@
 
 -   Problem formulation
 
--   Traditional clock skew scheduling ⏰
+-   Traditional clock skew scheduling ⌚
 
--   Yield-driven clock skew scheduling ⏰
+-   Yield-driven clock skew scheduling ⌚
 
 -   Minimum cost-to-time ratio cycle formulation
 
@@ -387,7 +387,7 @@
     -   (J. L. Neves and E. G. Friedman, "Optimal Clock Skew Scheduling
         Tolerant to Process Variations", DAC'96)
 -   Quadratic Programming method
-    -   (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⏰ for
+    -   (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⌚ for
         improved reliability via quadratic programming", ICCAD'99)
 
 Shortcoming: might reduce some slacks to be zero to minimum **total** CES.
@@ -399,7 +399,7 @@
 ----------------------
 
 -   Incremental Slack Distribution
-    -   (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⏰
+    -   (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⌚
         under process variations", ISQED'06)
 -   Advantage: check all skew constraints
 
diff --git a/algo4dfm/lec05a.md b/algo4dfm/lec05a.md
@@ -1,4 +1,4 @@
-# Lecture 05a - ⏰ Clock Skew Scheduling Under Process Variations
+# Lecture 05a - ⌚ Clock Skew Scheduling Under Process Variations
 
 @luk036
 
@@ -29,7 +29,7 @@ Overall, the lecture explores various techniques and methods for optimizing cloc
 - Useful skew design 有效偏差设计
   - Critical cycles 关键环
   - Negative cycles 负环
-- Clock skew scheduling ⏰ (CSS) 时钟偏差安排/规划
+- Clock skew scheduling ⌚ (CSS) 时钟偏差安排/规划
 - Yield-driven CSS 产品率驱动时钟偏差安排
 
 ## 🗺️ Overview
@@ -38,9 +38,9 @@ Overall, the lecture explores various techniques and methods for optimizing cloc
 
 - Problem formulation
 
-- Traditional clock skew scheduling ⏰
+- Traditional clock skew scheduling ⌚
 
-- Yield-driven clock skew scheduling ⏰
+- Yield-driven clock skew scheduling ⌚
 
 - Minimum cost-to-time ratio cycle formulation
 
@@ -269,7 +269,7 @@ variations](lec05.files/fig07.png)
   - (J. L. Neves and E. G. Friedman, "Optimal Clock Skew Scheduling
     Tolerant to Process Variations", DAC'96)
 - Quadratic Programming method
-  - (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⏰ for
+  - (I. S. Kourtev and E. G. Fredman, "Clock skew scheduling ⌚ for
     improved reliability via quadratic programming", ICCAD'99)
 
 Shortcoming: might reduce some slacks to be zero to minimum **total** CES.
@@ -278,7 +278,7 @@ This is not optimal for yield.
 ## Primitive solution (3)
 
 - Incremental Slack Distribution
-  - (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⏰
+  - (Xinjie Wei, Yici CAI and Xianlong Hong, "Clock skew scheduling ⌚
     under process variations", ISQED'06)
 - Advantage: check all skew constraints
 
diff --git a/algo4dfm/lec05b-remark.html b/algo4dfm/lec05b-remark.html
@@ -2,7 +2,7 @@
 <html>
   <head>
     <title>
-      Lecture 05b - ⏰ Clock Skew Scheduling Under Process Variations (2)
+      Lecture 05b - ⌚ Clock Skew Scheduling Under Process Variations (2)
     </title>
     <meta charset="utf-8" />
     <meta
@@ -29,7 +29,7 @@
 count: false
 class: nord-dark, middle, center
 
-Lecture 05b - ⏰ Clock Skew Scheduling Under Process Variations (2)
+Lecture 05b - ⌚ Clock Skew Scheduling Under Process Variations (2)
 ================================================================
 
 @luk036
diff --git a/algo4dfm/lec05b.md b/algo4dfm/lec05b.md
@@ -1,4 +1,4 @@
-# Lecture 05b - ⏰ Clock Skew Scheduling Under Process Variations (2)
+# Lecture 05b - ⌚ Clock Skew Scheduling Under Process Variations (2)
 
 ## 🗺️ Overview
 
@@ -161,7 +161,7 @@
 - Output:
   - Optimal t\* and its corresponding critical cycle C
 
-# ⏰ Clock Skew Scheduling for Unimodal Distributed Delay Models
+# ⌚ Clock Skew Scheduling for Unimodal Distributed Delay Models
 
 @luk036
 
diff --git a/algo4dfm/unimodal.html b/algo4dfm/unimodal.html
@@ -1,7 +1,7 @@
 <!doctype html>
 <html>
   <head>
-    <title>⏰ Clock Skew Scheduling for Unimodal Delay Models</title>
+    <title>⌚ Clock Skew Scheduling for Unimodal Delay Models</title>
     <meta charset="utf-8" />
     <meta
       name="viewport"
@@ -27,7 +27,7 @@
 count: false
 class: nord-dark, middle, center
 
-# ⏰ Clock Skew Scheduling for Unimodal Distributed Delay Models
+# ⌚ Clock Skew Scheduling for Unimodal Distributed Delay Models
 
 @luk036
 
