Lec00 generalized network flows

Lecture 0: Generalized Network Flows:

Theory, Algorithms, and Applications

Wai-Shing Luk (陆伟成)

Fudan University

2012年 8月 11日

W.-S. Luk (Fudan Univ.) Lecture 0: Generalized Network Flows 2012年 8月 11日 1 / 10

Motivation

Q. Why this topic is important?

A. Well, “network” is everywhere:

Transportation network, logistics network

Power network (smart grid)

Electronics circuits

Wireless network

Social network

Neural network, Bayesian network

and ...more


Motivation (cont’d)

Q. Why should I learn it as it is already a “mature” topic?

A. At least we still need to know

How to choose the existing algorithms wisely

How to transform a problem into a standard network flow formulation

How to handle new problems: e.g. non-linear problems.



Q. What are the limitations of the existing algorithms?

A. The existing algorithms

mostly handle linear problems, whereas most engineering problems are

non-linear.

can handle only single parameter (for parametric problems), whereas

most realistic problems are multi-parameter.

mostly rely on finding “cycles” rather than “cuts”. Dual problems are

first transformed into their primal counterparts via Lagrange duality

theory, which make the problem more complicated.



Q. Why should I learn this course instead of many others?

A In this course, we will

explain the concept using “Discrete Calculus”

describe how to transform a problem into a standard network flow

formulation.

describe the fundamental mechanism of algorithms so that we can

tackle new problems.


Why Generalization?

1 Unify network flows and physical flows. In fact, same terminology in

both sides is not coincident!

2 Develop co-domain algorithms for nonlinear scheduling problems.


Applications in Electronic Design Automation

Primal domain:

Escape routing (flip-chip)

Assignment problem

Resource allocation

Circuit partitioning

Bipartite matching

Perfect matching

Co-domain:

Clock skew scheduling

Re-timing

Delay padding

Buffer insertion

Transportation

Clock concurrent optimization


Theory

Discrete Calculus (1-complex = Network)

Concept of Pairing: Generalized Stokes’ theorem

Scheduling problem in co-domain

Important Note

Not direction, but orientation

Not duality, but pairing


Course Outline

Lecture 1: Network and flows

Lecture 2: feasibility problems

Lecture 3: Parametric problems (single parameter)

Lecture 4: Min-cost flow/potential problems (linear)

Lecture 5: Min-cost flow/potential problems (convex)

Lecture 6: Parametric problems (multi-parameter)


References

1 R. T. Rockafellar, Network flows and monotropic optimization, John Wiley

and & Sons, 1984.

2 Network optimization

3 Network flows: theory, algorithms and applications

4 S. M. Burns, Performance Analysis and Optimization of Asynchronous

Circuits. PhD thesis, CalTech, Pasadena, CA, December 1991.

5 N. E. Young, R. E. Tarjan, and J. B. Orlin, “Faster parametric shortest path

and minimum balance algorithms,” Networks, 1991.

6 Yi Wang, Wai-Shing Luk et al., Yield-driven clock skew scheduling

7 Yan-Ling Zhi, Wai-Shing Luk et al., Multi-domain clock skew scheduling


Lec00 generalized network flows

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