Related papers: Purification of large bicolorable graph states
Known entanglement purification protocols for mixed states use collective measurements on several copies of the state in order to increase the entanglement of some of them. We address the question of whether it is possible to purify the…
A proper vertex coloring of a graph is equitable if the sizes of all color classes differ by at most $1$. For a list assignment $L$ of $k$ colors to each vertex of an $n$-vertex graph $G$, an equitable $L$-coloring of $G$ is a proper…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…
Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual…
Reed [J.~Comb.~Theory B, 1999] showed that graphs of maximum degree $\Delta \geq 10^{14}$ without $\Delta$-cliques are $(\Delta-1)$-colorable. We design a one-pass semi-streaming algorithm for computing such a coloring. Additionally, we…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
We derive lower bounds for the attainable fidelity of standard entanglement purification protocols when local operations and measurements are subjected to errors. We introduce an error parameter which measures the distance between the ideal…
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of…
Gaussian graphical models represent the underlying graph structure of conditional dependence between random variables which can be determined using their partial correlation or precision matrix. In a high-dimensional setting, the precision…
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over…
We present the convergence study of a recurrence entanglement purification protocol using arbitrary two-qubit initial states. The protocol is based on a rank two projector in the Bell basis which serves as a two-qubit operation replacing…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
We study cutoff results for parameterized verification and synthesis of guarded protocols, as introduced by Emerson and Kahlon (2000). Guarded protocols describe systems of processes whose transitions are enabled or disabled depending on…
The paper presents techniques to derive upper bounds for the mean time to recover from a single fault for self-stabilizing algorithms in the message passing model. For a new Delta+1-coloring algorithm we analytically derive a bound for the…
An alternative presentation of the Oxford purification protocol is obtained by using dynamical variables. I suggest to introduce the degree of separability as a purification parameter, where the purified state has a smaller degree of…
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures.…
The paper deals with an extremal problem concerning colorings of hypergraphs with bounded edge degrees. Consider the family of $b$-simple hypergraphs, in which any two edges do not share more than $b$ common vertices. We prove that for…
A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Suppose that G is a planar graph with a maximum degree at most 5. We prove that G admits a…