The generalized dominance computation (GDC) problem is stated as follows: LetA= {a1, a2, …, an} be a set of triplets, i.e.,ai= (xi, yi,fi), “⊲” be a linear order relation defined on x-components, “<” be a linear order relation defined on y-components, and “⊕” an abelian operator defined onf-components. It is required to compute for everyai∈ A, the expressionD(ai)=fj1⊕fj2⊕ … ⊕ fjk, where {j1,j2, … jk{ is the set of all indicesjsuch thataj∈ Aandxj⊲ xi, yj< yi. First, this paper presents a time-optimal algorithm to solve the GDC problem inO(√n) on a mesh connected computer of size. √n× √n. To prove the generality of our approach, we show how a number of computational geometry problems, such as ECDF (empirical cumulative distribution function) searching and two-set dominance counting, can be derived from GDC problem. Second, we define a natural extension of the GDC, called mulliple-query generalized dominance computation (MQGDC), on meshes with multiple broadcasting. By using multiple querying (MQ) paradigm of Bokka et al. |3, 4, 6| we devise a time-optimal algorithm that solves a MQGDC problem involving a setAofnitems and a setQofmqueries inO(n⅙ ⅓) on a mesh with multiple broadcasting of size √n× √n.