Related papers: An enhanced formulation for solving graph coloring…
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…
Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this…
We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.
In this work, we present a branch-and-price algorithm to solve the weighted version of the List Coloring Problem, based on a vertex cover formulation by stable sets. This problem is interesting for its applications and also for the many…
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…
Graph coloring, also known as vertex coloring, considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the…
The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections…
We present an efficient algorithm for regularized optimal transport. In contrast to previous methods, we use the Douglas-Rachford splitting technique to develop an efficient solver that can handle a broad class of regularizers. The…
The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires…
In this paper, we present a Douglas-Rachford splitting algorithm within a Hilbert space framework that yields a projected solution for a quasi-variational inequality. This is achieved under the conditions that the operator associated with…
Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…
The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which…
The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that for all vertices v the color of v is different from the color of any of its neighbors. The problem is NP-hard.…
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…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
In this paper, we investigate the behavior of the family of graph-based splitting algorithms specialized to the problem of finding a point in the intersection of linear subspaces. The algorithms in this family, which encompasses several…
The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. For this NP-hard problem, a variety of integer linear…
In this expository paper, we show how to use the Douglas-Rachford algorithm as a successful heuristic for finding magic squares. The Douglas-Rachford algorithm is an iterative projection method for solving feasibility problems. Although its…