In allocation problems, a given set of goods are assigned to agents in such a way that the social welfare is maximised, that is, the largest possible global worth is achieved. When goods are indivisible, it is possible to use money compensation to perform a fair allocation taking into account the actual contribution of all agents to the social welfare. Coalitional games provide a formal mathema...

We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entry-wise `p-approximation error, for any p ≥ 1; the case p = 2 is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of lowrank approximation that work for every value of p ≥ 1, including p =∞. Our algorithms are simple, easy to implement, work...

In this paper we consider the continuous piecewise linear finite element approximation of the following problem: Given p € (1, oo), /, and g , find u such that -V • (\Vu\"-2Vu) = f iniîcR2, u = g on a«. The finite element approximation is defined over Í2* , a union of regular triangles, yielding a polygonal approximation to Q. For sufficiently regular solutions u , achievable for a subclass of ...

Let k be a number field, Ω be a finite symmetric subset of GLn0 (k), and Γ = 〈Ω〉. Let C(Γ) := {p ∈ Vf (k)| Γ is a bounded subgroup of GLn0 (kp)}, and Γp be the closure of Γ in GLn0 (kp). Assuming that the Zariski-closure of Γ is semisimple, we prove that the family of left translation actions {Γ y Γp}p∈C(Γ) has uniform spectral gap. As a corollary we get that the left translation action Γ y G h...

where Sn is the symmetric group of permutations on {1, 2, . . . , n}. Unlike the determinant, computing the exact value of the permanent of a given matrix is known to be #P-hard. Thus, most research has focused on finding approximation algorithms for and proving upper and lower bounds for restricted classes of matrices. A sharp upper-bound on the permanent the case of 0− 1 matrices was proved b...