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As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
A flow graph $G=(V,E,s)$ is a directed graph with a distinguished start vertex $s$. The dominator tree $D$ of $G$ is a tree rooted at $s$, such that a vertex $v$ is an ancestor of a vertex $w$ if and only if all paths from $s$ to $w$…
We consider the problem of forwarding packets arriving online with their destinations in a line network. In each time step, each router can forward one packet along the edge to its right. Each packet that is forwarded arrives at the next…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed…
Dense subgraph discovery is an important primitive in graph mining, which has a wide variety of applications in diverse domains. In the densest subgraph problem, given an undirected graph $G=(V,E)$ with an edge-weight vector $w=(w_e)_{e\in…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
While many graph drawing algorithms consider nodes as points, graph visualization tools often represent them as shapes. These shapes support the display of information such as labels or encode various data with size or color. However, they…
We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
We study the dispersion problem in anonymous port-labeled graphs: $k \leq n$ mobile agents, each with a unique ID and initially located arbitrarily on the nodes of an $n$-node graph with maximum degree $\Delta$, must autonomously relocate…
Consider the classical problem of information dissemination: one (or more) nodes in a network have some information that they want to distribute to the remainder of the network. In this paper, we study the cost of information dissemination…
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics. Many hard computational problems on graphs turn out to be efficiently solvable in…
To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to…
Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
Graph neural networks can be effectively applied to find solutions for many real-world problems across widely diverse fields. The success of graph neural networks is linked to the message-passing mechanism on the graph, however, the…