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Integrated Logistics PROBE

Integrated Logistics PROBE. Princeton University, 10/31-11/1. Presentation Outline. Defining Logistics Applications and Key Problems Facility Location Known Results Open Problems Hierarchical Network Design Known Results Open Problems. Defining Logistics.

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Integrated Logistics PROBE

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  1. Integrated Logistics PROBE Princeton University, 10/31-11/1

  2. Presentation Outline • Defining Logistics • Applications and Key Problems • Facility Location • Known Results • Open Problems • Hierarchical Network Design • Known Results • Open Problems

  3. Defining Logistics • Given service demands, must satisfy • “transporting products” from A to B • Goal is to minimize service cost • Aggregation problems

  4. Open facilities Each demand near to some facility Minimize sum or max distances Some restriction on facilities to open NP Hard (1.46) Facility Location Problems

  5. More than one level of “cluster” Basically building a tree or forest Solve FL over and over… but don’t want to pay much! Hierarchical Aggregation

  6. App: Trucking Service

  7. App: Trucking Service • Talk by Ted Gifford • Schneider Logistics • Multi-Billion dollar industry • Solve FL problems • Difficult to determine costs, constraints • Often solve problems exactly (IP) • Usually ~500-1000 nodes

  8. Open Problems: Trucking • Often multi-commodity FL • Hierarchical, but typically only 3-4 levels • Need extremely accurate solutions • “average case” bounds?

  9. App: Databases

  10. App: Databases • Talk by Sudipto Guha • U. Penn, AT&T research • Distributed databases • Determining data placement on network • Database Clustering • Many models, measures • Many different heuristics!

  11. Open Problems: Databases • Databases can be VERY large • “polynomial-time” not good enough • Streaming/sampling based approaches • Data may change with time • Need fast “update” algorithm • No clear measure of quality • “quick and dirty” may be best

  12. App: Genetics

  13. App: Genetics • Talk by Kamesh Munagala • Stanford University, Strand Genomics • Finding patterns in DNA/proteins • Known DNA code, but proteins mysterious • Can scan protein content of cells fast • Scan is not very accurate though • Find patterns in healthy vs. tumor cells

  14. Open Problems: Genetics • Huge amounts of data! • Also, not very accurate, many “mistakes” • Try to find separating dimension • Potentially many clusterings, find “best” • Really two-step problem • Find best “dimension” of exp. combinations • Cluster it, see if it separates

  15. Results: Facility Location • Talk by David Shmoys • Cornell University • Three main paradigms • Linear Program Rounding • Primal-Dual Method • Local Search

  16. Results: Facility Location • Talk by Kamal Jain • Microsoft Research • Talk by Mohammad Mahdian • MIT • Best approximation: 1.52 • Primal-dual based “greedy” algorithm • Solve LP to find “worst-case” approx

  17. Results: Facility Location • Talk by Martin Pal • Cornell University • Problem of FL with hard capacities • O(1) via local search • Open: O(1) via primal-dual or LP? • What is LP gap? • Often good to have “lower bound”

  18. Results: Facility Location • Talk by Ramgopal Mettu • Dartmouth University • FAST approximations for k-median • O(nk) constant approx • Repeated sampling approach • Compared to DB clustering heuristics • Slightly slower, much more accurate

  19. Open Problems: FL • Eliminate the gap! • 1.52 vs. 1.46, VERY close • Analysis of Mahdian is tight • Maybe time to revisit lower bound? • K-Median Problem • Local search gives 3, improve? • Load Balanced Problem • Exact on the lower bounds?

  20. Results: Network Design • Talk by Adam Meyerson • CMU • O(log n) for single-sink • O(log n log log n) for one function • O(1) for one sink, one function

  21. Results: Network Design • Talk by Kunal Talwar • UC Berkeley • Improved O(1) for one sink, function • LP rounding

  22. Results: Network Design • Connected Facility Location • Talks by Anupam Gupta • Lucent Research, CMU • Chaitanya Swamy • Cornell University • Give 9-approx for the problem • Greedy, primal-dual approaches

  23. Results: Network Design • Talk by Amitabh Sinha • CMU • Combining Buy-at-bulk with FL • O(log n) immediate, but what about O(1)? • O(1) for one cable type, small constant • O(1) in general • What about capacitated? K-med?

  24. Open Problems: ND • Multi-commodity, multiple function • No nontrivial approximations known! • O(1) for single sink? • LP gap not even known! • O(1) for single function? • Cannot depend on tree embedding • Make the constants reasonable! • Euclidean problem: easier?

  25. Conclusions • Many applications and open problems! • Must get in touch with DB community… • Workshop was a success, but… • Need more OR participation • Too short notice for faculty? • Plan another workshop, late March • Hope to have some more solutions!

  26. Thanks to Princeton Local Arrangements by Moses Charikar + Mitra Kelly

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