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On extreme points of the diffusion polytope

Author

Listed:
  • Hay, M.J.
  • Schiff, J.
  • Fisch, N.J.

Abstract

We consider a class of diffusion problems defined on simple graphs in which the populations at any two vertices may be averaged if they are connected by an edge. The diffusion polytope is the convex hull of the set of population vectors attainable using finite sequences of these operations. A number of physical problems have linear programming solutions taking the diffusion polytope as the feasible region, e.g. the free energy that can be removed from plasma using waves, so there is a need to describe and enumerate its extreme points. We review known results for the case of the complete graph Kn, and study a variety of problems for the path graph Pn and the cyclic graph Cn. We describe the different kinds of extreme points that arise, and identify the diffusion polytope in a number of simple cases. In the case of increasing initial populations on Pn the diffusion polytope is topologically an n-dimensional hypercube.

Suggested Citation

  • Hay, M.J. & Schiff, J. & Fisch, N.J., 2017. "On extreme points of the diffusion polytope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 225-236.
    • Handle: RePEc:eee:phsmap:v:473:y:2017:i:c:p:225-236
    DOI: 10.1016/j.physa.2017.01.038
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    References listed on IDEAS

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    1. Ronny Aboudi & Dominique Thon, 2008. "Second degree Pareto dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 475-493, April.
    2. Dhar, Deepak, 1999. "The Abelian sandpile and related models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 4-25.
    3. Dominique Thon & Stein W. Wallace, 2004. "Dalton transfers, inequality and altruism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 447-465, June.
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