capacity constrained network voronoi diagram (ccnvd)
DESCRIPTION
CAPACITY CONSTRAINED NETWORK VORONOI DIAGRAM (CCNVD). Presented by: GROUP 7 Gayathri Gandhamuneni & Yumeng Wang. AGENDA. Synonyms Definition Historical Background Scientific Fundamentals Key Applications Future Direction & References. SYNONYMS. CCNVD – None - PowerPoint PPT PresentationTRANSCRIPT
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CAPACITY CONSTRAINED NETWORK VORONOI DIAGRAM
(CCNVD)
Presented by:GROUP 7
Gayathri Gandhamuneni &Yumeng Wang
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AGENDA
SynonymsDefinitionHistorical BackgroundScientific FundamentalsKey ApplicationsFuture Direction & References
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SYNONYMS
CCNVD – None
Voronoi Diagram - Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation
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FORMAL DEFINITION
Capacity Constrained Network Voronoi Diagram (CCNVD):Partitions graph into set of contiguous service areas that honor service
center capacities and minimize the sum of distances from graph-nodes allotted service centers.
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SIGNIFICANCE & APPLICATIONSCritical Societal applicationsExamples:
Assigning consumers to gas stations in the aftermath of a disaster
Assigning evacuees to shelters Assigning patients to hospitalsAssigning students to school districts
CCNVDFinite SpacesContinuous Spaces
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PROBLEM STATEMENTInput:
A transportation network G – (Nodes N, Edges E)Set of service centers Constraints on the service centers Real weights on the edges.
Objective: Minimize the sum of distances from graph-nodes to their allotted service
centers while satisfying the constraints of the network. Constraints:
Nodes - Assumed to be contiguous The effective paths can be calculated (maximum coverage and shortest paths)
Output: Capacity Constrained Network Voronoi Diagram (CCNVD)
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HISTORICAL BACKGROUNDVoronoi Diagram:
Way of dividing space into a number of regionsA set of points (called seeds, sites, or generators) is specified beforehand
For each seed, there will be a corresponding region consisting of all points closer to that seed than to any other
Regions are called “Voronoi cells”
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RELATED WORKMinimizing sum of distances between graph nodes and their allotted service
centers
Honoring service center capacity
constraints
Service Area Contiguity
Min-cost flow approaches
Network Voronoi
Diagrams (NVD)CCNVD
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RELATED WORK ILLUSTRATION WITH DIAGRAMS
InputNVD
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RELATED WORK ILLUSTRATION WITH DIAGRAMS
Min-Cost Flow without SA contiguity(min-sum=30)(Output)
CCNVD (min-sum=30) (Output) – Pressure Equalizer Approach
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CHALLENGES
Large size of the transportation network
Uneven distribution - Service centers & Customers
Constraint: Service areas must be contiguous in graph to simplify communication
of allotments
NP Hard
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FUTURE DIRECTION
More factors of the problem into account Factors related to capacity of service centers,
Example:Number and distance of neighboring nodes Service quality of the service center.
Factors related to weight of each nodeNumber of consumersThe level of importance
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REFERENCES[1] KwangSoo Yang, Apurv Hirsh Shekhar, Dev Oliver, Shashi Shekhar: Capacity-Constrained Network-Voronoi Diagram: A Summary of Results. SSTD 2013: 56-73 [2] Advances in Spatial and Temporal Databases - 13th International Symposium, SSTD 2013 Munich, Germany, August 2013 Proceedings [3] http://en.wikipedia.org/wiki/Voronoi_diagram [4] Ahuja, R., Magnanti, T., Orlin, J.: Network flows: theory, algorithms, and applications, Prentice Hall [5] Goldberg, A.V., Tarjan, R.E.: Finding minimum-cost circulations by successive approximation. Mathematics of Operations Research 15(3), 430–466 (1990) [6] Klein, M.: A primal method for minimal cost flows with applications to the assignment and transportation problems. Management Science 14(3), 205–220 (1967) [7] Erwig, M.: The graph voronoi diagram with applications. Networks 36(3), 156–163 (2000) [8] Okabe, A., Satoh, T., Furuta, T., Suzuki, A., Okano, K.: Generalized network voronoi diagrams: Concepts, computational methods, and applications. International Journal of Geographical Information Science 22(9), 965–994 (2008)
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QUESTIONS?
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THANK YOU