Related papers: A Graph-Transformational Approach for Proving the …
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\cal…
The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we look at the link between the P - NP question and the "Deterministic" versus "Non Deterministic"…
In this paper, we critically examine Deng's "P=NP" [Den24]. The paper claims that there is a polynomial-time algorithm that decides 3-coloring for graphs with vertices of degree at most 4, which is known to be an NP-complete problem. Deng…
We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…
Graph Neural Networks (GNNs) are a form of deep learning that enable a wide range of machine learning applications on graph-structured data. The learning of GNNs, however, is known to pose challenges for memory-constrained devices such as…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
Inverse problems correspond to a certain type of optimization problems formulated over appropriate input distributions. Recently, there has been a growing interest in understanding the computational hardness of these optimization problems,…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous…
Recent years have witnessed the promise that reinforcement learning, coupled with Graph Neural Network (GNN) architectures, could learn to solve hard combinatorial optimization problems: given raw input data and an evaluator to guide the…
Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions,…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
For many fundamental problems in computational topology, such as unknot recognition and $3$-sphere recognition, the existence of a polynomial-time solution remains unknown. A major algorithmic tool behind some of the best known algorithms…
We introduce a novel framework of graph modifications specific to interval graphs. We study interdiction problems with respect to these graph modifications. Given a list of original intervals, each interval has a replacement interval such…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…