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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 University Three 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 based “greedy” algorithm Solve LP to find “worst-case” approx Primal-dual 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 log 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 + Mitra Kelly
