Integrated Logistics PROBE Princeton University, 10/31 -11/1
Presentation Outline ® Defining Logistics ® Applications and Key Problems ® Facility Location ® Known Results ® Open Problems ® Hierarchical ® Known Network Design Results ® Open Problems
Defining Logistics ® Given service demands, must satisfy ® “transporting products” from A to B ® Goal is to minimize service cost ® Aggregation problems
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)
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!
App: Trucking Service
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
Open Problems: Trucking ® Often multi-commodity FL ® Hierarchical, but typically only 3 -4 levels ® Need extremely accurate solutions ® “average case” bounds?
App: Databases
App: Databases ® Talk ® U. by Sudipto Guha Penn, AT&T research ® Distributed databases ® Determining ® Database ® Many data placement on network Clustering models, measures ® Many different heuristics!
Open Problems: Databases ® Databases can be VERY large ® “polynomial-time” not good enough ® Streaming/sampling based approaches ® Data may change with time ® Need ® No fast “update” algorithm clear measure of quality ® “quick and dirty” may be best
App: Genetics
App: Genetics ® Talk by Kamesh Munagala ® Stanford ® Finding University, Strand Genomics 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
Open Problems: Genetics ® Huge amounts of data! ® Also, ® Try not very accurate, many “mistakes” to find separating dimension ® Potentially ® Really ® Find many clusterings, find “best” two-step problem best “dimension” of exp. combinations ® Cluster it, see if it separates
Results: Facility Location ® Talk by David Shmoys ® Cornell ® Three University main paradigms ® Linear Program Rounding ® Primal-Dual Method ® Local Search
Results: Facility Location ® Talk by Kamal Jain ® Microsoft ® Talk Research by Mohammad Mahdian ® MIT ® Best approximation: 1. 52 ® Primal-dual based “greedy” algorithm ® Solve LP to find “worst-case” approx
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”
Results: Facility Location ® Talk by Ramgopal Mettu ® Dartmouth ® FAST University approximations for k-median ® O(nk) constant approx ® Repeated sampling approach ® Compared ® Slightly to DB clustering heuristics slower, much more accurate
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 ® Local ® Load Problem search gives 3, improve? Balanced Problem ® Exact on the lower bounds?
Results: Network Design ® Talk ® by Adam Meyerson CMU ® O(log n) for single-sink ® O(log n) for one function ® O(1) for one sink, one function
Results: Network Design ® Talk by Kunal Talwar ® UC Berkeley ® Improved ® LP O(1) for one sink, function rounding
Results: Network Design ® Connected ® Talks ® by Anupam Gupta Lucent Research, CMU ® Chaitanya ® Facility Location Swamy Cornell University ® Give 9 -approx for the problem ® Greedy, primal-dual approaches
Results: Network Design ® Talk by Amitabh Sinha ® CMU ® Combining ® O(log ® O(1) Buy-at-bulk with FL n) immediate, but what about O(1)? for one cable type, small constant ® O(1) in general ® What about capacitated? K-med?
Open Problems: ND ® Multi-commodity, ® No ® O(1) ® LP ® O(1) multiple function nontrivial approximations known! for single sink? gap not even known! for single function? ® Cannot ® Make depend on tree embedding the constants reasonable! ® Euclidean problem: easier?
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!
Thanks to Princeton Local Arrangements by Moses Charikar + Mi
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