Kostas Kolomvatsos, Kakia Panagidi, Stathes Hadjiefthymiades Pervasive Computing Research Group ( Department of Informatics and Telecommunications National and Kapodistrian University of Athens Optimal Spatial Partitioning for Resource Allocation ISCRAM 2013 Baden Baden, Germany

Outline Introduction Problem Formulation Data Organization Proposed approach Case Study

Introduction Spatial Partitioning Problem Segmentation of a geographical area Optimal allocation of a number of resources Resources could be vehicles, rescue teams, items, supplies, etc The allocation is done according to: Population patterns Spatial characteristics of the area The process is affected by the following issues: Where to locate the resources Which area each resource will cover The number of resources Final objective: to maximize the area that the limited number of resources will cover under a number of constraints.

Problem Formulation N j (j=1, 2, …, R, R is the resources number) resources are available to be allocated in an area A Each resource is of type T j The area has an orthogonal scheme (width: W 0, height: H 0 ) A number of constraints should be fulfilled (C jk, k=1,2, …, K) In the optimal solution, we have: where A l is the area covered by the l th resource. The shape of each sub-area is not defined Overlaps should be eliminated

Data Organization Area related parameters Population attributes, density of population Type of area (hilly, flat, etc) Roads – road segments (length, speed limit, width, type, etc), traffic Places of interest - PoIs (schools, hospitals, fuel stations, etc) Resource related parameters Type (e.g., vehicle, rescue team, supplies, etc) Maximum speed in emergency and maximum travel distance Crew or personnel Current Location Examples: Open Street Map could be the basis OSM data could be retrieved by CloudMade or Mapcruzin.com

Proposed Approach (1/2) Split the area Area A is defined by [(x UL, y UL ), (x LR, y LR )] – upper left and lower right corners Area A is divided into N c X N c cells Size of each cell Define cell weights Use of AHP for attributes priority Users define the relative weight for each attribute - criterion Cell weight calculation where w i is the i th attribute weight defined by AHP, A ij is the i th attribute value in cell j (e.g., schools, hospitals, fuel stations, etc), NA is the attributes number

Proposed Approach (2/2) Particle Swarm Optimization We generate M particles (M vectors p of all resources coordinates) p = [(x 1, y 1 ), (x 2, y 2 ), …, (x N, y N )] Coordinates are the center of a specific cell Fitness Function F(p): Covered Area by each particle (each resource) The best solution p* maximizes F(p*) If we consider that resources are vehicles Area covered by a resource T: time restriction, S: maximum speed, w i : the weight of each cell in the neighbor, NH: number of neighbors Total covered area by the particle, |Ns i |: neighbors number

Case Study (1/2) Suppose N j = 5 ambulances are available Their characteristics are: We define maximum response time T = 5 minutes We select the desired area NoCapacityMax speed (Km/h)Max travel distance (Km)

Case Study (2/2) Resource locations are presented in the map Numerical Results

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