Suchisman Gangopadhyay Montgomery High School, New Jersey

Planning Troop & Resource Deployments at Military Bases using Exponentially WeightedVoronoi DiagramsAbstract 1106 for WG-16 Presented at 2013 81.1 MORS ConferenceMay 14, 2013 @ 1400 Hrs EDT Suchisman Gangopadhyay Montgomery High School, New Jersey Admitted as Freshman, University of Illinois, Urbana-Champaign suchismangang@gmail.com Suchisman Gangopadhyay

Premise • Troop Deployment and Voronoi • Insurgent Activity and Weighted Voronoi • Boulding’s Loss of Strength Gradient and Exponential Weightage • Method • Observations & Results • Next steps • References Outline Suchisman Gangopadhyay

Premise Suchisman Gangopadhyay

Due to the unpredictable nature of war, reducing the time this process takes can win battles and save lives Deciding on how many resources to send to a military base is a time consuming process Suchisman Gangopadhyay

One of the methods of determining these areas is to use Voronoi Diagrams Assuming uniform land structure, resources can be deployed based on how much land each base must administer Suchisman Gangopadhyay

A cell is formed around each site, consisting of the points which are closest to that site. Points on cell walls are equally close to two sites, while points on vertices are equally close to three or more sites Voronoi Diagrams tessellate a plane into sections based on how close parts of the plane are to certain points, called sites Suchisman Gangopadhyay

Resources can then be distributed in the ratio of areas of the sites The positions of the bases can be used as sites to create a Voronoi diagram Suchisman Gangopadhyay

A base in a safer area may receive the same amount of resources as a base that has to protect regions that are constantly under attack Unfortunately, this method does not account for the uneven presence of insurgents Suchisman Gangopadhyay

If a normal Voronoi uses the simple distance formula, then a weighted Voronoi uses a weight to modify that distance The use of a weighted Vornonoi can account for this Suchisman Gangopadhyay

Other types of weighting have each site holding a different weightage, which is then added, multiplied, etc. to a distance between some point and that site One frequent type of distance formula often substituted for the regular distance formula is “Manhattan distance” Suchisman Gangopadhyay

He argued that the strength of a military force was related to the distance that force had to travel In 1962, Kenneth Boulding devised a loss of strength gradient Suchisman Gangopadhyay

Due to the use of exponents in this gradient, it makes sense for the weightage used in this Voronoi to be exponential The loss of strength gradient can be expressed as: Suchisman Gangopadhyay

Method Suchisman Gangopadhyay

Step 1: Plot the coordinates of the bases on a Cartesian plane (represented by blue stars) Suchisman Gangopadhyay

Step 2: Use a Voronoi tessellation to find the land each base administers Suchisman Gangopadhyay

Step 3: Add locations of insurgent activity to the Voronoi (represented by orange dots Suchisman Gangopadhyay

Step 4: Find the concentration of enemy activity in each cell Suchisman Gangopadhyay

Step 5: Use these concentrations as weightages to create an exponentially weighted Voronoi Suchisman Gangopadhyay

Observations & Results Suchisman Gangopadhyay

Step 6: Distribute resources using the ratios of the area of the weighted cells a. Ratio is calculated as the number of points plotted in each weighted Voronoi cell by MATLAB ®. Suchisman Gangopadhyay

While still accounting for how much land each base must administer This method results in more resources being given to bases in the middle of enemy activity Suchisman Gangopadhyay

When making an exponentially weighted Voronoi diagram, there are a few things one must look out for Suchisman Gangopadhyay

Therefore, it is important to be consistent with units when constructing the diagram First, exponentially weighted Voronoi diagrams differ by scale Suchisman Gangopadhyay

A cell seeming like it is subsumed within another may actually be much bigger Next, there are some strange structures one may see when creating an exponential Voronoi Suchisman Gangopadhyay

Next Steps Suchisman Gangopadhyay

By using the deployment of resources in successful operations as an example, the formula for weightage can be adjusted to replicate those results Exponential weightage is only the beginning Suchisman Gangopadhyay

Instead of starting with a regular Voronoi, the land each base administers could be split based on a Voronoi weighted to account for uneven territory Another way this method can become more accurate and versatile is to account for natural formations and enemy structures Suchisman Gangopadhyay

The quicker the algorithm for creating these weighted Voronoi diagrams is, the quicker one can respond to new information Lastly, while simple and additively weighted Voronoi diagrams can be constructed efficiently, other types of weighted Voronoi diagrams can take much longer to create Suchisman Gangopadhyay

Thanks! Q & A Suchisman Gangopadhyay

K. Boulding, Conflict and Defense, Harper, New York, 1962, 262. • K. Boulding, The Meaning of the 20th Century, The Great Transition, George Allen & Unwin, London, 1965, 87 • A.G. Boyer, N.J. Gauthier, and C.W. Johnson, The Paradoxes of Military Risk Assessment, In Proceedings of the 25th International Systems Safety Conference, Baltimore, USA, International Systems Safety Society, Unionville, VA, USA, 859-869, 0-9721385-7-9, 2007 • B. B. de Mesquita, The War Trap, Yale University Press, New Haven, 1981, 103-108 • D. Lemke, Regions of War and Peace, Press Syndicate of the University of Cambridge, Cambridge, England, 2002, 71-73 • J.D. Vanvactor, Risk Mitigation Through a Composite Risk Management Process, The U.S. Army Risk Assessment Organization Development Journal Vol. 25 Nbr. (2007) • K. Webb, The Continued Importance of Geographic Distance and Boulding's Loss of Strength Gradient, Comparative Strategy, Volume 26 Issue 4, 2007, 295-310 References Suchisman Gangopadhyay

Suchisman Gangopadhyay Montgomery High School, New Jersey