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Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…
We consider the distributed weight balancing problem in networks of nodes that are interconnected via directed edges, each of which is able to admit a positive integer weight within a certain interval, captured by individual lower and upper…
Random walk based sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as GMD modify the topology of…
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
Unlike conventional "black-box" transformers with classical self-attention mechanism, we build a lightweight and interpretable transformer-like neural net by unrolling a mixed-graph-based optimization algorithm to forecast traffic with…
We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least $(1-\eps)$…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
A mixed dominating set of a graph $G = (V, E)$ is a mixed set $D$ of vertices and edges, such that for every edge or vertex, if it is not in $D$, then it is adjacent or incident to at least one vertex or edge in $D$. The mixed domination…
We study text summarization from the viewpoint of maximum coverage problem. In graph theory, the task of text summarization is regarded as maximum coverage problem on bipartite graph with weighted nodes. In recent study, belief-propagation…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
In the online bipartite matching with reassignments problem, an algorithm is initially given only one side of the vertex set of a bipartite graph; the vertices on the other side are revealed to the algorithm one by one, along with its…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M…
We present a simple nonadaptive randomized algorithm that estimates the number of edges in a simple, unweighted, undirected graph, possibly containing isolated vertices, using only degree and random edge queries. For an $n$-vertex graph,…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
The notion of forbidden-transition graphs allows for a robust generalization of walks in graphs. In a forbidden-transition graph, every pair of edges incident to a common vertex is permitted or forbidden; a walk is compatible if all pairs…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…