Network flow algorithms
David P. Williamson.
Bok Engelsk 2019 · Electronic books.
| Utgitt | Cambridge University Press
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|---|---|
| Omfang | 1 online resource (xii, 314 pages) : : digital, PDF file(s).
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| Utgave | 1st ed.
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| Opplysninger | Title from publisher's bibliographic system (viewed on 26 Aug 2019).. - Cover -- Half-title -- Frontispiece -- Title page -- Copyright information -- Contents -- Preface -- Acknowledgments -- 1 Preliminaries: Shortest Path Algorithms -- 1.1 Nonnegative Costs: Dijkstra's Algorithm -- 1.2 Negative Costs: The Bellman-Ford Algorithm -- 1.3 Negative-Cost Cycle Detection -- Exercises -- Chapter Notes -- 2 Maximum Flow Algorithms -- 2.1 Optimality Conditions -- 2.2 Application: Carpool Sharing -- 2.3 Application: The Baseball Elimination Problem -- 2.4 Application: Finding a Maximum Density Subgraph -- 2.5 Most Improving Augmenting Paths -- 2.6 A Capacity Scaling Algorithm -- 2.7 Shortest Augmenting Paths -- 2.8 The Push-Relabel Algorithm -- Exercises -- Chapter Notes -- 3 Global Minimum Cut Algorithms -- 3.1 The Hao-Orlin Algorithm -- 3.2 The MA Ordering Algorithm -- 3.3 The Random Contraction Algorithm -- 3.4 The Gomory-Hu Tree -- Exercises -- Chapter Notes -- 4 More Maximum Flow Algorithms -- 4.1 Blocking Flows -- 4.2 Blocking Flows in Unit Capacity Graphs -- 4.3 The Goldberg-Rao Algorithm -- Exercises -- Chapter Notes -- Permissions -- 5 Minimum-Cost Circulation Algorithms -- 5.1 Optimality Conditions -- 5.2 Wallacher's Algorithm -- 5.3 Minimum-Mean Cycle Canceling -- 5.4 A Capacity Scaling Algorithm -- 5.5 Successive Approximation -- 5.6 Network Simplex -- 5.7 Application: Maximum Flow Over Time -- Exercises -- Chapter Notes -- 6 Generalized Flow Algorithms -- 6.1 Optimality Conditions -- 6.2 A Wallacher-Style GAP-Canceling Algorithm -- 6.3 Negative-Cost GAP Detection -- 6.4 Lossy Graphs, Truemper's Algorithm, and Gain Scaling -- 6.5 Error Scaling -- Exercises -- Chapter Notes -- 7 Multicommodity Flow Algorithms -- 7.1 Optimality Conditions -- 7.2 The Two-Commodity Case -- 7.3 Intermezzo: The Multiplicative Weights Algorithm -- 7.4 The Garg-Könemann Algorithm -- 7.5 The Awerbuch-Leighton Algorithm -- Exercises.. - Chapter Notes -- 8 Electrical Flow Algorithms -- 8.1 Optimality Conditions -- 8.2 Maximum Flow in Undirected Graphs -- 8.3 Graph Sparsification -- 8.4 A Simple Laplacian Solver -- Exercises -- Chapter Notes -- Permissions -- 9 Open Questions -- References -- Author Index -- Index.. - Network flow theory has been used across a number of disciplines, including theoretical computer science, operations research, and discrete math, to model not only problems in the transportation of goods and information, but also a wide range of applications from image segmentation problems in computer vision to deciding when a baseball team has been eliminated from contention. This graduate text and reference presents a succinct, unified view of a wide variety of efficient combinatorial algorithms for network flow problems, including many results not found in other books. It covers maximum flows, minimum-cost flows, generalized flows, multicommodity flows, and global minimum cuts and also presents recent work on computing electrical flows along with recent applications of these flows to classical problems in network flow theory.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 1-316-88856-8
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