Integrated Logistics PROBE

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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 dont want to pay
  much!

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App Trucking Service
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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

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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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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!

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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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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

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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