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Integrated Logistics PROBE

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Title: Integrated Logistics PROBE


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
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)

5
Hierarchical Aggregation
  • More than one level of cluster
  • Basically building a tree or forest
  • Solve FL over and over but dont want to pay
    much!

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, ATT 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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