  In order to guarantee the downloading quality requirements of users and
improve the stability of data transmission in a BitTorrent-like peer-to-peer
file sharing system, this article deals with eigenproblems of addition-min
algebras. First, it provides a sufficient and necessary condition for a vector
being an eigenvector of a given matrix, and then presents an algorithm for
finding all eigenvalues and eigenvectors of a given matrix. It further proposes
a sufficient and necessary condition for a vector being a constrained
eigenvector of a given matrix and supplies an algorithm for computing all the
constrained eigenvectors and eigenvalues of a given matrix. This article
finally discusses the supereigenproblem of a given matrix and presents an
algorithm for obtaining the maximum constrained supereigenvalue and depicting
the feasible region of all the constrained supereigenvectors for a given
matrix. It also gives some examples for illustrating the algorithms,
respectively.
