Let G be an unweighted graph of complexity n embedded in a surface of genus g, orientable or not. We describe improved algorithms to compute a shortest non-contractible and a shor...
In this paper we study a fundamental open problem in the area of probabilistic checkable proofs: What is the smallest s such that NP naPCP1,s[O(log n), 3]? In the language of har...
We show that for k ≥ 3 even the Ω(n) level of the Lasserre hierarchy cannot disprove a random k-CSP instance over any predicate type implied by k-XOR constraints, for example ...
An approximation algorithm for a constraint satisfaction problem is said to be nontrivial if its performance ratio is strictly superior to the expected performance of the algorith...
Stone-Weierstrass-type theorems for groups of group-valued functions with discrete range or discrete domain are obtained. We study criteria for a subgroup of the group of continuou...