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Integrated Logistics PROBE Princeton University, 10/31-11/1
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Presentation Outline Defining Logistics Applications and Key Problems Facility Location Known Results Open Problems Hierarchical Network Design Known Results Open Problems
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Defining Logistics Given service demands, must satisfy “transporting products” from A to B Goal is to minimize service cost Aggregation problems
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Facility Location Problems Open facilities Each demand near to some facility Minimize sum or max distances Some restriction on facilities to open NP Hard (1.46)
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Hierarchical Aggregation More than one level of “cluster” Basically building a tree or forest Solve FL over and over… but don’t want to pay much!
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App: Trucking Service
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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
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Open Problems: Trucking Often multi-commodity FL Hierarchical, but typically only 3-4 levels Need extremely accurate solutions “average case” bounds?
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App: Databases
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Talk by Sudipto Guha U. Penn, AT&T research Distributed databases Determining data placement on network Database Clustering Many models, measures Many different heuristics!
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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
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App: Genetics
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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
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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
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Results: Facility Location Talk by David Shmoys Cornell University Three main paradigms Linear Program Rounding Primal-Dual Method Local Search
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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
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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”
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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
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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?
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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
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Results: Network Design Talk by Kunal Talwar UC Berkeley Improved O(1) for one sink, function LP rounding
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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
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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?
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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?
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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!
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Thanks to Princeton Local Arrangements by Moses Charikar + Mitra Kelly
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