We consider the computational complexity of the market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.

We consider the complexity of combining bodies of evidence according to the rules of the Dempster{Shafer theory of evidence. We prove that, given as input a set of tables representing basic probability assignments m1; : : : ; mn over a frame of discernment , and a set A , the problem of computing the combined basic probability value (m1: : :mn)(A) is #P-complete. As a corollary, we obtain that ...

Given a function f over n binary variables, and an ordering of the n variables, Added abstract we consider the Expected Decision Depth problem. Namely, what is the expected number of bits that need to be observed until the value of the function is determined, when bits of the input are observed according to the given order. Our main finding is that this problem is #P-hard. In particular, hardne...

In this paper we prove that calculating the average covering tree value recently proposed as a single-valued solution of graph games is #P-complete.

We introduce in this chapter A generalization of the classical collineation of P n. The generalization allows for a certain degree of freedom in the local-ization of points in P n at the expense of using multiple m > 2 views. The degree of freedom per point is governed by an additional parameter 1 ≤ k < n which stands for the dimension of the subspace in which the indvidual points are allowed t...