Integrated Logistics PROBE Princeton University, 10/31-11/1
Dec 22, 2015
Presentation OutlineDefining LogisticsApplications and Key ProblemsFacility Location
Known Results Open Problems
Hierarchical Network Design Known Results Open Problems
Defining LogisticsGiven service demands, must satisfy “transporting products” from A to BGoal is to minimize service costAggregation 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 ServiceTalk by Ted Gifford
Schneider LogisticsMulti-Billion dollar industrySolve FL problems
Difficult to determine costs, constraints Often solve problems exactly (IP) Usually ~500-1000 nodes
Open Problems: TruckingOften multi-commodity FLHierarchical, but typically only 3-4 levelsNeed extremely accurate solutions
“average case” bounds?
App: DatabasesTalk by Sudipto Guha
U. Penn, AT&T researchDistributed databases
Determining data placement on networkDatabase Clustering
Many models, measures Many different heuristics!
Open Problems: DatabasesDatabases 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: GeneticsTalk by Kamesh Munagala
Stanford University, Strand GenomicsFinding 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: GeneticsHuge 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 LocationTalk by David Shmoys
Cornell UniversityThree main
paradigms Linear Program
Rounding Primal-Dual Method Local Search
Results: Facility LocationTalk by Kamal Jain
Microsoft ResearchTalk by Mohammad Mahdian
MITBest approximation: 1.52
Primal-dual based “greedy” algorithm Solve LP to find “worst-case” approx
Results: Facility LocationTalk by Martin Pal
Cornell UniversityProblem of FL with hard capacitiesO(1) via local searchOpen: O(1) via primal-dual or LP?
What is LP gap? Often good to have “lower bound”
Results: Facility LocationTalk by Ramgopal Mettu
Dartmouth UniversityFAST approximations for k-median
O(nk) constant approx Repeated sampling approach
Compared to DB clustering heuristics Slightly slower, much more accurate
Open Problems: FLEliminate 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 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 DesignTalk by Kunal Talwar
UC Berkeley
Improved O(1) for one sink, function LP rounding
Results: Network DesignConnected 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 DesignTalk by Amitabh Sinha
CMUCombining Buy-at-bulk with FL
O(log n) immediate, but what about O(1)?O(1) for one cable type, small constantO(1) in generalWhat about capacitated? K-med?
Open Problems: NDMulti-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 embeddingMake the constants reasonable!Euclidean problem: easier?
ConclusionsMany 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!