Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...

We present a greedy algorithm that determines a lower bound on the zero error capacity. The algorithm has many new advantages, e.g., it does not store a whole product graph in a computer memory and it uses the so-called distributions in all dimensions to get a better approximation of the zero error capacity. We also show an additional application of our algorithm.

We present a greedy algorithm that determines a lower bound on the zero error capacity. The algorithm has many new advantages, e.g., it does not store a whole product graph in a computer memory and it uses the so-called distributions in all dimensions to get a better approximation of the zero error capacity. We also show an additional application of our algorithm.

The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory...

Consider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target vertex in a graph by asking queries. Each query is conducted as follows: the strategy selects a vertex q and receives a reply v: if q is the target, then =, and if q is not the target, then v is a...