  We conjecture that the discrete light-cone quantization (DLCQ) of strings on
the maximally supersymmetric type IIB plane-wave background in the sector with
J units of light-cone momentum is a supersymmetric 0+1 dimensional U(J) gauge
theory (quantum mechanics) with PSU(2|2)x PSU(2|2)x U(1) superalgebra. The
conjectured Hamiltonian for the plane-wave matrix (string) theory, the tiny
graviton matrix theory, is the quantized (regularized) three brane action on
the same background. We present some pieces of evidence for this conjecture
through analysis of the Hamiltonian, its vacua, spectrum and coupling constant.
Moreover, we discuss an extension of our conjecture to the DLCQ of type IIB
strings on AdS_5 x S^5 geometry.
