Related papers: A Near-Real-Time Reduction-Based Algorithm for Col…
Recommendation algorithm plays an important role in recommendation system (RS), which predicts users' interests and preferences for some given items based on their known information. Recently, a recommendation algorithm based on the graph…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
In this paper, we revisit the online recoloring problem introduced recently by Azar et al. In online recoloring, there is a fixed set $V$ of $n$ vertices and an initial coloring $c_0: V\rightarrow [k]$ for some $k\in \mathbb{Z}^{>0}$. Under…
Register allocation is one of the most important problems for modern compilers. With a practically unlimited number of user variables and a small number of CPU registers, assigning variables to registers without conflicts is a complex task.…
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel…
We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…
Node coloring is the task of assigning colors to the nodes of a graph such that no two adjacent nodes have the same color, while using as few colors as possible. It is the most widely studied instance of graph coloring and of central…
A classic graph coloring problem is to assign colors to vertices of any graph so that distinct colors are assigned to adjacent vertices. Optimal graph coloring colors a graph with a minimum number of colors, which is its chromatic number.…
Decolorization is the process to convert a color image or video to its grayscale version, and it has received great attention in recent years. An ideal decolorization algorithm should preserve the original color contrast as much as…
We present a new algorithm for the exact uniform sampling of proper \(k\)-colorings of a graph on \(n\) vertices with maximum degree~\(\Delta\). The algorithm is based on partial rejection sampling (PRS) and introduces a soft relaxation of…
Problems involving multiple networks are prevalent in many scientific and other domains. In particular, network alignment, or the task of identifying corresponding nodes in different networks, has applications across the social and natural…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
We show how graph neural networks can be used to solve the canonical graph coloring problem. We frame graph coloring as a multi-class node classification problem and utilize an unsupervised training strategy based on the statistical physics…
Combinatorial optimization problem (COP) over graphs is a fundamental challenge in optimization. Reinforcement learning (RL) has recently emerged as a new framework to tackle these problems and has demonstrated promising results. However,…
In the $\ell$-Coloring Problem, we are given a graph on $n$ nodes, and tasked with determining if its vertices can be properly colored using $\ell$ colors. In this paper we study below-guarantee graph coloring, which tests whether an…