Related papers: Planar Network Diversion
The mobile robot 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…
Min orderings give a vertex ordering characterization, common to some graphs and digraphs such as interval graphs, complements of threshold tolerance graphs (known as co-TT graphs), and two-directional orthogonal ray graphs. An adjusted…
We consider the following fundamental routing problem. An adversary inputs packets arbitrarily at sources, each packet with an arbitrary destination. Traffic is constrained by link capacities and buffer sizes, and packets may be dropped at…
Graph learning is the fundamental task of estimating unknown graph connectivity from available data. Typical approaches assume that not only is all information available simultaneously but also that all nodes can be observed. However, in…
The network unreliability problem asks for the probability that a given undirected graph gets disconnected when every edge independently fails with a given probability $p$. Valiant (1979) showed that this problem is \#P-hard; therefore, the…
In today's world, modern infrastructures are being equipped with information and communication technologies to create large IoT networks. It is essential to monitor these networks to ensure smooth operations by detecting and correcting link…
Graph Neural Networks (GNNs) have shown promising results in modeling graphs in various tasks. The training of GNNs, especially on specialized tasks such as bioinformatics, demands extensive expert annotations, which are expensive and…
Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…
Emerging networked systems become increasingly flexible and reconfigurable. This introduces an opportunity to adjust networked systems in a demand-aware manner, leveraging spatial and temporal locality in the workload for online…
Graph Neural Networks (GNNs) are state-of-the-art models for performing prediction tasks on graphs. While existing GNNs have shown great performance on various tasks related to graphs, little attention has been paid to the scenario where…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
In the $k$-dispersion problem, we need to select $k$ nodes of a given graph so as to maximize the minimum distance between any two chosen nodes. This can be seen as a generalization of the independent set problem, where the goal is to…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
The girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev,…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
In this paper we study graph problems in dynamic streaming model, where the input is defined by a sequence of edge insertions and deletions. As many natural problems require $\Omega(n)$ space, where $n$ is the number of vertices, existing…
Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios,…
Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of…
We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time…
Graph-based Neural Networks (GNNs) are recent models created for learning representations of nodes (and graphs), which have achieved promising results when detecting patterns that occur in large-scale data relating different entities. Among…