This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
An Efficient Simplex Coverability Algorithm in E2 with Application to Stochastic Sequential Machines
February 1979 (vol. 28 no. 2)
pp. 109-120
C.B., Jr. Silio, Department of Electrical Engineering, University of Maryland
The problem of determining the existence of a simplex which covers a given convex polytope inside another given convex polytope in two-dimensional Euclidean space is shown to be efficiently solvable, and an effective procedure is derived to find a suitable covering simplex or show that none exists. This solution provides a finite algorithm for satisfying a necessary condition in the search for a simplicial (fewest states) stochastic sequential machine (SSM) which either covers or is covered by a given SSM of rank three. Theorems are proved which establish necessary and sufficient conditions restricting the class of corresponding simplexes through which a search must proceed to those whose vertices lie in the boundary of the bounding polytope and whose facet-supporting flats contain certain specified vertices of the polytope to be covered. The problem is then reduced to testing roots in the finite solution tree of a set of second degree algebraic equations against a finite table of linear constraints. An algorithm to generate the constraint sets for the equations to be solved is also presented along with examples of its application.
Index Terms:
simplex covering, Computational complexity, covering problems, convex polytopes, finite search procedure, geometric programming, probabilistic automata
Citation:
C.B., Jr. Silio, "An Efficient Simplex Coverability Algorithm in E2 with Application to Stochastic Sequential Machines," IEEE Transactions on Computers, vol. 28, no. 2, pp. 109-120, Feb. 1979, doi:10.1109/TC.1979.1675300
Usage of this product signifies your acceptance of the Terms of Use.