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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…
This work presents the first study of using the popular Monte Carlo Tree Search (MCTS) method combined with dedicated heuristics for solving the Weighted Vertex Coloring Problem. Starting with the basic MCTS algorithm, we gradually…
A Neighborhood Balanced Coloring (NBC) of a graph is a red-blue coloring where each vertex has the same number of red and blue neighbors. This work proves that determining if a graph admits an NBC is NP-complete. We present a genetic…
A $b$-coloring of a graph is a proper vertex coloring such that each color class contains a vertex that sees all other colors in its neighborhood. The $b$-coloring problem, in which the task is to decide whether a graph admits a…
Maximum Common induced Subgraph (MCS) is an important NP-hard problem with wide real-world applications. Branch-and-Bound (BnB) is the basis of a class of efficient algorithms for MCS, consisting in successively selecting vertices to match…
Error correction at short blocklengths remains a challenge for low-density parity-check (LDPC) codes, as belief propagation (BP) decoding is suboptimal compared to maximum-likelihood decoding (MLD). While BP rarely makes errors, it often…
The vertex coloring problem has received a lot of attention in the context of synchronous round-based systems where, at each round, a process can send a message to all its neighbors, and receive a message from each of them. Hence, this…
In recent years, there has been a significant amount of research focused on expanding the expressivity of Graph Neural Networks (GNNs) beyond the Weisfeiler-Lehman (1-WL) framework. While many of these studies have yielded advancements in…
Exemplar-based colorization approaches rely on reference image to provide plausible colors for target gray-scale image. The key and difficulty of exemplar-based colorization is to establish an accurate correspondence between these two…
The Balanced Connected Subgraph problem (BCS) was recently introduced by Bhore et al. (CALDAM 2019). In this problem, we are given a graph $G$ whose vertices are colored by red or blue. The goal is to find a maximum connected subgraph of…
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…
Population-based memetic algorithms have been successfully applied to solve many difficult combinatorial problems. Often, a population of fixed size was used in such algorithms to record some best solutions sampled during the search.…
Given an undirected graph $G=(V,E)$ with a set of vertices $V$ and a set of edges $E$, a graph coloring problem involves finding a partition of the vertices into different independent sets. In this paper we present a new framework that…
In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color…
This work explores how to design a single neural network capable of adapting to multiple heterogeneous vision tasks, such as image segmentation, 3D detection, and video recognition. This goal is challenging because both network architecture…
Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem…
Among the limitations of current quantum machines, the qubits count represents one of the most critical challenges for porting reasonably large computational problems, such as those coming from real-world applications, to the scale of the…
We study the behavior of the Douglas-Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In…
The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem. Recently there has been great interest in solving this problem on real-world massive graphs. For such graphs, local search is a promising approach to finding optimal…
We present a polynomial-time algorithm that colors any 3-colorable $n$-vertex graph using $O(n^{0.19539})$ colors, improving upon the previous best bound of $\widetilde{O}(n^{0.19747})$ by Kawarabayashi, Thorup, and Yoneda [STOC 2024]. Our…