  A very brief introduction to tropical and idempotent mathematics is
presented. Tropical mathematics can be treated as a result of a dequantization
of the traditional mathematics as the Planck constant tends to zero taking
imaginary values. In the framework of idempotent mathematics usually
constructions and algorithms are more simple with respect to their traditional
analogs. We especially examine algorithms of tropical/idempotent mathematics
generated by a collection of basic semiring (or semifield) operations and other
"good" operations. Every algorithm of this type has an interval version. The
complexity of this interval version coincides with the complexity of the
initial algorithm. The interval version of an algorithm of this type gives
exact interval estimates for the corresponding output data. Algorithms of
linear algebra over idempotent and semirings are examined. In this case, basic
algorithms are polynomial as well as their interval versions. This situation is
very different from the traditional linear algebra, where basic algorithms are
polynomial but the corresponding interval versions are NP-hard and interval
estimates are not exact.
