Related papers: Variations on Memetic Algorithms for Graph Colorin…
Based on the framework of the quantum-inspired evolutionary algorithm, a cuckoo quantum evolutionary algorithm (CQEA) is proposed for solving the graph coloring problem (GCP). To reduce iterations for the search of the chromatic number, the…
We investigate the algorithmic problems of the {\it homophyly phenomenon} in networks. Given an undirected graph $G = (V, E)$ and a vertex coloring $c \colon V \rightarrow {1, 2, ..., k}$ of $G$, we say that a vertex $v\in V$ is {\it happy}…
he greatest weakness of evolutionary algorithms, widely used today, is the premature convergence due to the loss of population diversity over generations. To overcome this problem, several algorithms have been proposed, such as the…
Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these…
One method to obtain a proper vertex coloring of graphs using a reasonable number of colors is to start from any arbitrary proper coloring and then repeat some local re-coloring techniques to reduce the number of color classes. The Grundy…
The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied…
We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for $(\Delta+1)$- vertex coloring and…
We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX-$k$-CUT, the problem of finding an approximate $k$-vertex coloring of a graph. We compare this proposal to the best known classical and hybrid…
We develop a heuristic graph coloring approximation algorithm that uses the D-Wave 2X as an independent set sampler and evaluate its performance against a fully classical implementation. A randomly generated set of small but hard graph…
Graph algorithms mainly belong to two categories, topology-driven and data-driven. Data-driven approach maintains a worklist of active nodes, the nodes on which work has to be done. Topology-driven approach sweeps over the entire graph to…
Register allocation, which is a crucial phase of a good optimizing compiler, relies on graph coloring. Hence, an efficient graph coloring algorithm is of paramount importance. In this work we try to learn a good heuristic for coloring…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
In vertex recoloring, we are given $n$ vertices with their initial coloring, and edges arrive in an online fashion. The algorithm must maintain a valid coloring by recoloring vertices, at a cost. The problem abstracts a scenario of job…
A proper coloring $c$ of a simple graph $G$ is harmonious if, for every pair of distinct edges $uv,xy\in E(G)$, we have that $\{c(u),c(v)\}\neq \{c(x),c(y)\}$. The harmonious chromatic number of $G$, denoted by $h(G)$, is the least positive…
Graph colorings is a fundamental topic in graph theory that require an assignment of labels (or colors) to vertices or edges subject to various constraints. We focus on the harmonious coloring of a graph, which is a proper vertex coloring…
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…
Vizing's theorem states that any graph of maximum degree $\Delta$ can be properly edge colored with at most $\Delta+1$ colors. In the online setting, it has been a matter of interest to find an algorithm that can properly edge color any…
Neutral atom arrays have emerged as a versatile candidate for the embedding of hard classical optimization problems. Prior work has focused on mapping problems onto finding the maximum independent set of weighted or unweighted unit disk…
We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different…
Given an undirected graph $G$, the Minimum Sum Coloring problem (MSCP) is to find a legal assignment of colors (represented by natural numbers) to each vertex of $G$ such that the total sum of the colors assigned to the vertices is…