Related papers: Local Routing in Graphs Embedded on Surfaces of Ar…
We study online graph queries that retrieve nearby nodes of a query node from a large network. To answer such queries with high throughput and low latency, we partition the graph and process the data in parallel across a cluster of servers.…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
Graph Representation Learning (GRL) has experienced significant progress as a means to extract structural information in a meaningful way for subsequent learning tasks. Current approaches including shallow embeddings and Graph Neural…
Large scale decentralized communication systems have introduced the new trend towards online routing where routing decisions are performed based on a limited and localized knowledge of the network. Geometrical greedy routing has been among…
Learning node representations is a fundamental problem in graph machine learning. While existing embedding methods effectively preserve local similarity measures, they often fail to capture global functions like graph distances. Inspired by…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
We give an algorithm to calculate the minimal and maximal genus of the orientable closed surface where a graph $G$ can be embedded. For this, we construct some special branched coverings of the 2-sphere. We apply this algorithm to calculate…
The dispersion problem on graphs asks $k\leq n$ robots placed initially arbitrarily on the nodes of an $n$-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This…
Read-only memory model is a classical model of computation to study time-space tradeoffs of algorithms. One of the classical results on the ROM model is that any sorting algorithm that uses O(s) words of extra space requires $\Omega…
Social network analysis provides meaningful information about behavior of network members that can be used for diverse applications such as classification, link prediction. However, network analysis is computationally expensive because of…
Geographic routing is becoming the protocol of choice for many sensor network applications. The current state of the art is unsatisfactory: some algorithms are very efficient, however they require a preliminary planarization of the…
Representation learning on graphs, also called graph embedding, has demonstrated its significant impact on a series of machine learning applications such as classification, prediction and recommendation. However, existing work has largely…
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps, which constructs a graph embedding…
Let $G$ be an edge-weighted directed graph with $n$ vertices embedded on an orientable surface of genus $g$. We describe a simple deterministic lexicographic perturbation scheme that guarantees uniqueness of minimum-cost flows and shortest…
The in-memory graph layout or organization has a considerable impact on the time and energy efficiency of distributed memory graph computations. It affects memory locality, inter-task load balance, communication time, and overall memory…
The $2$-cell embeddings of graphs on closed surfaces have been widely studied. It is well known that ($2$-cell) embedding a given graph $G$ on a closed orientable surface is equivalent to cyclically ordering the edges incident to each…
Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three…
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be…
Existing graph clustering networks heavily rely on a predefined yet fixed graph, which can lead to failures when the initial graph fails to accurately capture the data topology structure of the embedding space. In order to address this…
Graph neural networks (GNNs) have achieved success in various inference tasks on graph-structured data. However, common challenges faced by many GNNs in the literature include the problem of graph node embedding under various geometries and…