LP Rounding for Poise

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Gives an LP rounding algorithm that produces a spanning (or Steiner) tree whose sum of diameter and maximum degree (poise) is within O(log n) of the LP optimum. Key steps: use matching-based augmentation to reduce components, formulate a path-length-bounded flow LP that routes terminals to connectors, scale and filter long fractional paths, apply a path-packing plus column-sparsity rounding to get integral short paths with bounded node congestion, then extract a BFS tree to bound diameter and degree.

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" chapters (18)

1. 0:00Intro
2. 0:36Minimum Poise Trees
3. 2:54Outline
4. 3:14Matching Based Augmentation
5. 4:40Example: log, n approximation for Minimum Spanning Tree
6. 5:34A Tree-Pairing Lemma
7. 8:07Proposed Application
8. 10:49Algorithm Sketch
9. 13:33Simple fix
10. 15:07Diameter-bounded min-degree trees
11. 18:25LP for Steiner Poise L
12. 20:42Use MBA strategy for poise
13. 20:52T-path packing
14. 23:58Use a Filtered LP solution
15. 24:34Rounding Flow Paths
16. 28:27A new spanning tree objective
17. 29:35Multi-commodity Multicast
18. 30:16Related Work