[PPT] - Theory and Algorithms of Physical Design C.K. Cheng, T.C. Hu, and PowerPoint Presentation

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Theory and Algorithms of Physical Design

C.K. Cheng, T.C. Hu, and A.B. Kahng CSE department UC San Diego

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Biography of T.C. Hu
Physical Design
Column Generating Techniques
Motto
Sequencing
Pick’s Theorem
Bin Packing
Logic and Reasoning
Min Cut
Conclusion

OUTLINES

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BIOGRAPHY OF T.C. HU

1968-1974 Professor, Computer

Sciences Department and Mathematics Research Center, University of Wisconsin-Madison

1974-1998 Professor, Department
f Computer Science and

Engineering, University of California, San Diego

1998-2007 Professor, Above-

Scale, Department of Computer Science and Engineering, University of California, San Diego

1954-1956 Programmer, University of Illinois
1964-1965 Visiting Associate Professor, Electrical Engineering and

Operations Research Center, University of California, Berkeley (on leave from IBM)

1965-1966 Adjunct Associate Professor, Columbia University (part-time)
1966-1968 Associate Professor, University of Wisconsin

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A pioneer in combinatorial algorithms, mathematical

programming and operations research.

He published the Gomory-Hu cut tree on multi-

terminal flows, at IBM Research Center.

His works cover multicommodity flows, job

scheduling, decomposition for distributed computation, integer programming, tree structures, matrix chain product, knapsack problems, routing, and many other fundamental topics.

He and his Ph.D. student M. T. Shing applied routing

to VLSI layout problems, 1984.

T.C. HU: PHYSICAL DESIGN

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In T.C. Hu and E. S. Kuh, “VLSI Circuit Layout: Theory and Design”, IEEE Press, 1985, he raised the question, “Is there an algorithm which can be proved mathematically?” Since many physical design problems are NP-complete, most of the proposed ingenious algorithms tend to be heuristic. The question was met with a positive, “yes” response using an example of column-generating techniques for global routing. The analogy of traffic congestion was used to formulate the routing problem as a multicommodity network flow problem with duality and shadow price to reflect the cost

f the traffic jams on each channel (street). A column

generating technique was introduced to derive the error bound of the solution.

COLUMN GENERATING TECHNIQUES

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Through his career, Prof. Hu’s techniques of mathematical programming and combinatorics have enriched the theory and methods of physical design. His works contribute to the physical design in tree representation, partitioning, and routing. Moreover, he also provided insight and recipes for successful research. The shadow price highlights the importance to view problems from different angles. His motto, “always start with the simplest nontrivial cases,” fits well with physical design, where the problem tends to be complex and at the same time the geometry of the layout provides us with insight into the solution.

“ALWAYS START WITH THE SIMPLEST NONTRIVIAL CASES” – T. C. HU

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QUIZZES (INDIAN LECTURES)

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A coin has two faces. A toss of the coin lands either Head

r Tail. Two sequences, say HHHH, or HHTH. Then the

subsequence appears first wins.

NOT ALL SEQUENCES ARE CREATED EQUAL

H H H T H T

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A toss of the coin lands either Head or Tail. Two sequences, say HHHH, or HHTH. Then the subsequence appears first wins.

NOT ALL SEQUENCES ARE CREATED EQUAL

H S H H

T T T H/1

H S H T

T H T H/1

Different diagrams yield different expectations

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What is the area of a room? Count the number of adults inside, add half of the boys on the wall, and subtract the

ne just left.

PICK’S THEOREM

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What is the area of a room? Count the number of adults inside, add half of the boys on the wall, and subtract the

ne just left.

PICK’S THEOREM 7+8/2-1= 10 7 adults 8 boys

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Mother bought back five cakes each weighing one ounce, two weighing two ounces, and one weighing four ounces. Mother said eat as much as you can, but do not pick up another piece until you have finished the one you have. Assume that two children have the same speed of eating.

BIN PACKING

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Mother bought back five cakes each weighing one ounce, two weighing two ounces, and one weighing four ounces.

BIN PACKING 1, 2, 2, 4 Pick 1 first?

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There is an island occupied by two tribes, the truth teller and the liar. Once, a visitor came to the island meeting two persons, A and B from each tribe, respectively. A said “one

f us is a liar.” B said “he is a liar.” Based on the above

conversation, can you find out who is the liar?

LOGIC AND REASONING

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There is an island occupied by two tribes, the truth teller and the liar. Once, a visitor came to the island meeting two persons, A and B from each tribe, respectively. A said “one

f us is a liar.” B said “he is a liar.” Based on the above

conversation, can you find out who is the liar?

LOGIC AND REASONING

If B tells the truth, then A’s statement is also true, which hints A is not a liar. Thus, B is a liar.

Derive by Contradiction:

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A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

1 5 6 7 8 2 3 4 2 3 4 3 1 3 3 2 2 2 2 2

Problem: Find the minimum of the max-flow min-cuts among all pairs (without calculating the network flow!).

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A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

1 5 6 7 8 2 3 4 2 3 4 3 1 3 3 2 2 2 2 2

Problem: Find the minimum of the max-flow min-cuts among all pairs (without calculating the network flow!).

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A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

1 5 6 7 8 2 3 4 2 3 4 3 1 3 3 2 2 2 2 2

Problem: Find the minimum of the max-flow min-cuts among all pairs (without calculating the network flow!). Starting from one node (2), cluster the most adjacent node. Repeat until all the nodes are clustered. The last two nodes are either on the same side of the minimum cut or forming the cut.

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A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

1,5 6 7 8 2 3 4 3 4 3 1 3 2 2 2 4 2 1 5 6 7 8 2 3 4 2 3 4 3 1 3 3 2 2 2 2 2

Starting from one node (2), cluster the most adjacent node. Repeat until all the nodes are clustered. The last two nodes are either on the same side of the minimum cut or form the cut.

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A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

1,5 6 7,8 2 3 4 3 4 3 1 2 2 4 4

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A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

1,5 6 4,7 8 2 3 3 3 1 2 6 4 1,5 6 2 3,4 7,8 3 3 2 4 1

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Computational Complexity: O(|V||E|+|V|log|V|)

MINIMUM CUT (MAXIMUM FLOW)

1,5 3,4 6,7,8 2 3 5 4 V-2 2 9

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Foundation of theory and

algorithms

Don’t be intimidated by NP-

Completeness

Curiosity and fun
Collaboration
Always start with the

simplest nontrivial cases

CONCLUSION

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Theory and Algorithms of Physical Design

C.K. Cheng, T.C. Hu, and A.B. Kahng CSE department UC San Diego

OUTLINES

BIOGRAPHY OF T.C. HU

Sciences Department and Mathematics Research Center, University of Wisconsin-Madison

Engineering, University of California, San Diego

Scale, Department of Computer Science and Engineering, University of California, San Diego

Operations Research Center, University of California, Berkeley (on leave from IBM)

programming and operations research.

terminal flows, at IBM Research Center.

scheduling, decomposition for distributed computation, integer programming, tree structures, matrix chain product, knapsack problems, routing, and many other fundamental topics.

to VLSI layout problems, 1984.

T.C. HU: PHYSICAL DESIGN

generating technique was introduced to derive the error bound of the solution.

COLUMN GENERATING TECHNIQUES

“ALWAYS START WITH THE SIMPLEST NONTRIVIAL CASES” – T. C. HU

QUIZZES (INDIAN LECTURES)

A coin has two faces. A toss of the coin lands either Head

subsequence appears first wins.

NOT ALL SEQUENCES ARE CREATED EQUAL

H H H T H T

A toss of the coin lands either Head or Tail. Two sequences, say HHHH, or HHTH. Then the subsequence appears first wins.

NOT ALL SEQUENCES ARE CREATED EQUAL

H S H H

H S H T

Different diagrams yield different expectations

What is the area of a room? Count the number of adults inside, add half of the boys on the wall, and subtract the

PICK’S THEOREM

What is the area of a room? Count the number of adults inside, add half of the boys on the wall, and subtract the

PICK’S THEOREM 7+8/2-1= 10 7 adults 8 boys

Mother bought back five cakes each weighing one ounce, two weighing two ounces, and one weighing four ounces. Mother said eat as much as you can, but do not pick up another piece until you have finished the one you have. Assume that two children have the same speed of eating.

BIN PACKING

Mother bought back five cakes each weighing one ounce, two weighing two ounces, and one weighing four ounces.

BIN PACKING 1, 2, 2, 4 Pick 1 first?

There is an island occupied by two tribes, the truth teller and the liar. Once, a visitor came to the island meeting two persons, A and B from each tribe, respectively. A said “one

conversation, can you find out who is the liar?

LOGIC AND REASONING

There is an island occupied by two tribes, the truth teller and the liar. Once, a visitor came to the island meeting two persons, A and B from each tribe, respectively. A said “one

conversation, can you find out who is the liar?

LOGIC AND REASONING

If B tells the truth, then A’s statement is also true, which hints A is not a liar. Thus, B is a liar.

Derive by Contradiction:

A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

Problem: Find the minimum of the max-flow min-cuts among all pairs (without calculating the network flow!).

A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

Problem: Find the minimum of the max-flow min-cuts among all pairs (without calculating the network flow!).

MINIMUM CUT (MAXIMUM FLOW)

Problem: Find the minimum of the max-flow min-cuts among all pairs (without calculating the network flow!). Starting from one node (2), cluster the most adjacent node. Repeat until all the nodes are clustered. The last two nodes are either on the same side of the minimum cut or forming the cut.

MINIMUM CUT (MAXIMUM FLOW)

Starting from one node (2), cluster the most adjacent node. Repeat until all the nodes are clustered. The last two nodes are either on the same side of the minimum cut or form the cut.

A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

A simple cut algorithm by M. Stoer and F. Wagner, Journal of the ACM, pp 585-591, July 1997.

MINIMUM CUT (MAXIMUM FLOW)

Computational Complexity: O(|V||E|+|V|log|V|)

MINIMUM CUT (MAXIMUM FLOW)

algorithms

Completeness

simplest nontrivial cases

CONCLUSION

Thank you!