Related papers: A Near-Real-Time Reduction-Based Algorithm for Col…
A new algorithm for exactly sampling from the set of proper colorings of a graph is presented. This is the first such algorithm that has an expected running time that is guaranteed to be linear in the size of a graph with maximum degree \(…
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all…
Graph analysis is a critical component of applications such as online social networks, protein interactions in biological networks, and Internet traffic analysis. The arrival of massive graphs with hundreds of millions of nodes, e.g. social…
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…
In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve a…
Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal…
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…
We develop the first parallel graph coloring heuristics with strong theoretical guarantees on work and depth and coloring quality. The key idea is to design a relaxation of the vertex degeneracy order, a well-known graph theory concept, and…
Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at…
The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve…
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 resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…
In this paper, we consider distributed coloring for planar graphs with a small number of colors. We present an optimal (up to a constant factor) $O(\log{n})$ time algorithm for 6-coloring planar graphs. Our algorithm is based on a novel…
The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in…
We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Vizing's celebrated theorem states that every simple graph with maximum degree $\Delta$ admits a $(\Delta+1)$ edge coloring which can be found in $O(m \cdot n)$ time on $n$-vertex $m$-edge graphs. This is just one color more than the…
Several recent results from dynamic and sublinear graph coloring are surveyed. This problem is widely studied and has motivating applications like network topology control, constraint satisfaction, and real-time resource scheduling. Graph…
One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…