Related papers: Euler Meets GPU: Practical Graph Algorithms with T…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
In the present paper we give an explicit formula which allows us immediately to describe a unique Gauss circuit on a framed 4-valent graph (a graph with a structure of opposite edges) from an arbitrary Euler tour on the graph whenever the…
Evolutionary computing (EC) has proven to be effective in solving complex optimization and robotics problems. Unfortunately, typical Evolutionary Algorithms (EAs) are constrained by the computational capacity available to researchers. More…
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 this paper we obtain the expectation and variance of the number of Euler tours of a random Eulerian directed graph with fixed out-degree sequence. We use this to obtain the asymptotic distribution of the number of Euler tours of a random…
The increasing scale and wealth of inter-connected data, such as those accrued by social network applications, demand the design of new techniques and platforms to efficiently derive actionable knowledge from large-scale graphs. However,…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Motivated by generalizations of de Bruijn cycles to various combinatorial structures (Chung, Diaconis, and Graham), we study various Euler tours in set systems. Let $\mathcal{G}$ be a hypergraph whose corank and rank are $c\geq 3$ and $k$,…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available…
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…
Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of…
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the…
We study a multimodal journey planning scenario consisting of a public transit network and a transfer graph which represents a secondary transportation mode (e.g., walking, cycling, e-scooter). The objective is to compute Pareto-optimal…
Community detection now is an important operation in numerous graph based applications. It is used to reveal groups that exist within real world networks without imposing prior size or cardinality constraints on the set of communities.…
Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…