  The effects of the generalized uncertainty principle({\bf GUP}) on the
cosmological constant problem are discussed in the Schwarzchild-deSitter
spacetime, through studying the corrections to its thermodynamics. We derive
the correction to the Hawking temperature of the cosmological horizon, by a
heuristic method enlighten by gr-qc/0106080 . The logarithmic correction to the
Bekenstein-Hawking entropy is also obtained. For an ordinary star (not a black
hole), the probable ratio of the vacuum energy to the total energy within the
cosmological horizon is 2/3, which roughly coincides with the evidences from
the astronomical observations. For a black hole, the ratio tends to decrease.
An inequality associating the energy density with the length of system is put
forward for understanding the smallness of the cosmological constant, and the
relation between the Bekenstein entropy bound and the Bekenstein-Hawking
entropy is also briefly discussed.
