  We construct an Imbimbo-Mukhi type matrix model, which reproduces exactly the
partition function of ${\mathbb{CP}^1}$ topological strings in the small phase
space, Nekrasov's instanton counting in ${\cal{N}}=2$ gauge theory and the
large $N$ limit of the partition function in 2-dimensional Yang-Mills theory on
a sphere. In addition, we propose a dual Stieltjes-Wigert type matrix model,
which emerges when all-genus topological string amplitudes on certain simple
toric Calabi-Yau manifolds are compared with the Imbimbo-Mukhi type model.
