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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 Network Design Known Results Open Problems. Defining Logistics.

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integrated logistics probe

Integrated Logistics PROBE

Princeton University, 10/31-11/1

presentation outline
Presentation Outline
  • Defining Logistics
  • Applications and Key Problems
  • Facility Location
    • Known Results
    • Open Problems
  • Hierarchical Network Design
    • Known Results
    • Open Problems
defining logistics
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)

Facility Location Problems
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!

Hierarchical Aggregation
app trucking service1
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
Open Problems: Trucking
  • Often multi-commodity FL
  • Hierarchical, but typically only 3-4 levels
  • Need extremely accurate solutions
    • “average case” bounds?
app databases1
App: Databases
  • Talk by Sudipto Guha
    • U. Penn, AT&T research
  • Distributed databases
    • Determining data placement on network
  • Database Clustering
    • Many models, measures
    • Many different heuristics!
open problems databases
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
app genetics1
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
open problems genetics
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
results facility location
Results: Facility Location
  • Talk by David Shmoys
    • Cornell University
  • Three main paradigms
    • Linear Program Rounding
    • Primal-Dual Method
    • Local Search
results facility location1
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
results facility location2
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 location3
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
open problems fl
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?
results network design
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 design1
Results: Network Design
  • Talk by Kunal Talwar
    • UC Berkeley
  • Improved O(1) for one sink, function
    • LP rounding
results network design2
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
results network design3
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?
open problems nd
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?
conclusions
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
Thanks to Princeton

Local Arrangements by Moses Charikar + Mitra Kelly