Related papers: Constructing Basis Path Set by Eliminating Path De…

Based on basis path set, G-SGD algorithm significantly outperforms conventional SGD algorithm in optimizing neural networks. However, how the inner mechanism of basis paths work remains mysterious. From the aspect of graph theory, this…

In recent years, various deep learning architectures have been proposed to solve complex challenges (e.g. spatial dependency, temporal dependency) in traffic domain, which have achieved satisfactory performance. These architectures are…

Dense subgraph discovery is a fundamental problem in graph mining with a wide range of applications \cite{gionis2015dense}. Despite a large number of applications ranging from computational neuroscience to social network analysis, that take…

Two subsets of a given set are path-disconnected if they lie in different connected components of the larger set. Verification of path-disconnectedness is essential in proving the infeasibility of motion planning and trajectory optimization…

Graph neural networks (GNN) has been successfully applied to operate on the graph-structured data. Given a specific scenario, rich human expertise and tremendous laborious trials are usually required to identify a suitable GNN architecture.…

The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the well-known d-separation criterion. It allows us to build graphical representations of dependency models (usually probabilistic…

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct pairs. We determine, with an exception of two cases, the complexity of the…

Finding a simple path of even length between two designated vertices in a directed graph is a fundamental NP-complete problem known as the EvenPath problem. Nedev proved in 1999, that for directed planar graphs, the problem can be solved in…

Degree-based graph construction is an ubiquitous problem in network modeling, ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive…

This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…

Graph Neural Networks (GNNs) is an architecture for structural data, and has been adopted in a mass of tasks and achieved fabulous results, such as link prediction, node classification, graph classification and so on. Generally, for a…

Two fundamental algorithm-design paradigms are Tree Search and Dynamic Programming. The techniques used therein have been shown to complement one another when solving the complete set partitioning problem, also known as the coalition…

We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…

Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…

Motivated by hybrid graph representations, we introduce and study the following beyond-planarity problem, which we call $h$-Clique2Path Planarity: Given a graph $G$, whose vertices are partitioned into subsets of size at most $h$, each…

Code search aims to retrieve accurate code snippets based on a natural language query to improve software productivity and quality. With the massive amount of available programs such as (on GitHub or Stack Overflow), identifying and…

One or more searchers must capture an invisible evader hiding in the nodes of a graph. We study this graph search problem; we emphasize that we study the capture of a node-located evader, which has received less attention than edge search.…

Shortest path search is a core operation in graph-based applications, yet existing methods face important limitations. Classical algorithms such as Dijkstra's and A* become inefficient as graphs grow more complex, while index-based…

Graph Neural Networks (GNNs) are gaining extensive attention for their application in graph data. However, the black-box nature of GNNs prevents users from understanding and trusting the models, thus hampering their applicability. Whereas…

This paper builds on recent developments in Bayesian network (BN) structure learning under the controversial assumption that the input variables are dependent. This assumption can be viewed as a learning constraint geared towards cases…