- Play ►
### Introduction and Probability Review

01:16:27Robert GallagerWe 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.

- Play ►
### More Review: The Bernoulli Process

01:08:20Robert GallagerWe 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.

- Play ►
### Law of Large Numbers, Convergence

01:21:28Robert GallagerWe 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.

- Play ►
### Poisson (the Perfect Arrival Process)

01:17:14Robert Gallager - Play ►
### Poisson Combining and Splitting

01:24:32Robert Gallager - Play ►
### From Poisson to Markov

01:19:17Robert Gallager - Play ►
### Finite-state Markov Chains: The Matrix Approach

00:55:34Robert Gallager - Play ►
### Markov Eigenvalues and Eigenvectors

01:23:38Robert Gallager - Play ►
### Markov Rewards and Dynamic Programming

01:23:36Robert Gallager - Play ►
### Renewals and the Strong Law of Large Numbers

01:21:53Robert Gallager - Play ►
### Renewals: Strong Law and Rewards

01:18:17Robert Gallager - Play ►
### Renewal Rewards, Stopping Trials, and Wald's Inequality

01:26:22Robert Gallager - Play ►
### Little, M/G/1, Ensemble Averages

01:14:53Robert Gallager - Play ►
### The Last Renewal

01:15:44Robert Gallager - Play ►
### Renewals and Countable-State Markov

01:19:40Robert Gallager - Play ►
### Countable-State Markov Chains

01:23:46Robert Gallager - Play ►
### Countable-State Markov Chains and Processes

01:16:29Robert Gallager - Play ►
### Countable-State Markov Processes

01:22:15Robert Gallager - Play ►
### Markov Processes and Random Walks

01:23:09Robert Gallager - Play ►
### Hypothesis Testing and Random Walks

01:25:23Robert Gallager - Play ►
### Random Walks and Thresholds

01:21:17Robert Gallager - Play ►
### Martingales (Plain, Sub, and Super)

01:22:40Robert Gallager - Play ►
### Martingales: Stopping and Converging

01:20:44Robert Gallager - Play ►
### Putting It All Together

01:21:27Robert Gallager

Home > Mathematics > Calculus > Discrete Stochastic Processes Lectures: