Related papers: Minimizing LR(1) State Machines is NP-Hard
This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…
We consider the robustness of computational hardness of problems whose input is obtained by applying independent random deletions to worst-case instances. For some classical $NP$-hard problems on graphs, such as Coloring, Vertex-Cover, and…
Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization…
Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
In the Minimum Bisection problem, input is a graph $G$ and the goal is to partition the vertex set into two parts $A$ and $B$, such that $||A|-|B|| \le 1$ and the number $k$ of edges between $A$ and $B$ is minimized. This problem can be…
We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to…
We present a novel neural architecture to solve graph optimization problems where the solution consists of arbitrary node labels, allowing us to solve hard problems like graph coloring. We train our model using reinforcement learning,…
Abstract Meaning Representation (AMR) parsing aims to extract an abstract semantic graph from a given sentence. The sequence-to-sequence approaches, which linearize the semantic graph into a sequence of nodes and edges and generate the…
Many NP-hard graph problems become easy for some classes of graphs. For example, coloring is easy for bipartite graphs, but NP-hard in general. So we can ask question like when does a hard problem become easy? What is the minimum…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
In Defective Coloring we are given a graph $G$ and two integers $\chi_d$, $\Delta^*$ and are asked if we can $\chi_d$-color $G$ so that the maximum degree induced by any color class is at most $\Delta^*$. We show that this natural…
Deep reinforcement learning (RL) methods often require many trials before convergence, and no direct interpretability of trained policies is provided. In order to achieve fast convergence and interpretability for the policy in RL, we…
The \(L_1/L_2\) norm ratio has gained significant attention as a measure of sparsity due to three merits: sharper approximation to the \(L_0\) norm compared to the \(L_1\) norm, being parameter-free and scale-invariant, and exceptional…
Restricted star colouring is a variant of star colouring introduced to design heuristic algorithms to estimate sparse Hessian matrices. For $k\in\mathbb{N}$, a $k$-restricted star colouring ($k$-rs colouring) of a graph $G$ is a function…
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…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
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…
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.…
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in…