相关论文: Minimizing LR(1) State Machines is NP-Hard

We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…

We study a very restrictive graph exploration problem. In our model, an agent without persistent memory is placed on a vertex of a graph and only sees the adjacent vertices. The goal is to visit every vertex of the graph, return to the…

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal…

The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L$_1$ regularization is used to remove the spurious weak connections that would otherwise be found by simply minimizing…

Large Language Models (LLMs) have shown strong capabilities in solving problems across domains, including graph-related tasks traditionally addressed by symbolic or algorithmic methods. In this work, we present a framework for structured…

The anti-Ramsey number, $ar(G, H)$ is the minimum integer $k$ such that in any edge colouring of $G$ with $k$ colours there is a rainbow subgraph isomorphic to $H$, i.e., a copy of $H$ with each of its edges assigned a different colour. The…

In this paper we introduce and study a new problem named \emph{min-max edge $q$-coloring} which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer $q$. The goal is…

We present a two-step hybrid reinforcement learning (RL) policy that is designed to generate interpretable and robust hierarchical policies on the RL problem with graph-based input. Unlike prior deep reinforcement learning policies…

We study a combinatorial problem arising from microarrays synthesis. The synthesis is done by a light-directed chemical process. The objective is to minimize unintended illumination that may contaminate the quality of experiments.…

Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…

Large Language Models (LLMs) for Graph Reasoning have been extensively studied over the past two years, involving enabling LLMs to understand graph structures and reason on graphs to solve various graph problems, with graph algorithm…

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the…

A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a…

There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…

We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…

This paper studies the kernelization complexity of graph coloring problems with respect to certain structural parameterizations of the input instances. We are interested in how well polynomial-time data reduction can provably shrink…

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with…

The paper deals with extremal problems concerning colorings of hypergraphs. By using a random recoloring algorithm we show that any $n$-uniform simple (i.e. every two distinct edges share at most one vertex) hypergraph $H$ with maximum edge…

A class domination coloring (also called cd-Coloring or dominated coloring) of a graph is a proper coloring in which every color class is contained in the neighbourhood of some vertex. The minimum number of colors required for any…

We present a simple linear programming (LP) based method to learn compact and interpretable sets of rules encoding the facts in a knowledge graph (KG) and use these rules to solve the KG completion problem. Our LP model chooses a set of…