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### Introduction and Lumped Abstraction

00:41:08Anant AgarwalWe revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

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### Basic Circuit Analysis Method (KVL and KCL mMethod)

00:49:09Anant AgarwalWe revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

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### Superposition, Thevenin and Norton

00:51:11Anant AgarwalWe revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

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### The Digital Abstraction

00:49:06Anant Agarwal - Play ►
### Inside the Digital Gate

00:51:05Anant Agarwal - Play ►
### Nonlinear Analysis

00:44:50Anant Agarwal - Play ►
### Incremental Analysis

00:50:10Anant Agarwal - Play ►
### Dependent Sources and Amplifiers

00:52:23Anant Agarwal - Play ►
### MOSFET Amplifier Large Signal Analysis, Part 1

00:50:33Anant Agarwal - Play ►
### MOSFET Amplifier Large Signal Analysis, Part 2

00:50:33Anant Agarwal - Play ►
### Amplifiers - Small Signal Model

00:50:30Anant Agarwal - Play ►
### Small Signal Circuits

00:50:03Anant Agarwal - Play ►
### Capacitors and First-Order Systems

00:49:09Anant Agarwal - Play ►
### Digital Circuit Speed

00:52:50Anant Agarwal - Play ►
### State and Memory

00:48:00Anant Agarwal - Play ►
### Second-Order Systems, Part 1

00:50:09Anant Agarwal - Play ►
### Second-Order Systems, Part 2

00:50:10Anant Agarwal - Play ►
### Sinusoidal Steady State

00:52:07Anant Agarwal - Play ►
### The Impedance Model

00:49:30Anant Agarwal - Play ►
### Filters

00:47:58Anant Agarwal - Play ►
### The Operational Amplifier Abstraction

00:52:31Anant Agarwal - Play ►
### Operational Amplifier Circuits

00:49:51Anant Agarwal - Play ►
### Op Amps Positive Feedback

00:51:13Anant Agarwal - Play ►
### Energy and Power

00:51:41Anant Agarwal - Play ►
### Energy, CMOS

00:40:11Anant Agarwal - Play ►
### Violating the Abstraction Barrier

00:46:36Anant Agarwal