Related papers: Shortest node-disjoint paths on random graphs
We study distributed optimization problems over a network when the communication between the nodes is constrained, and so information that is exchanged between the nodes must be quantized. This imperfect communication poses a fundamental…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
The advancement of mobile technologies and the proliferation of map-based applications have enabled a user to access a wide variety of services that range from information queries to navigation systems. Due to the popularity of map-based…
Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…
Gossip algorithms have recently received significant attention, mainly because they constitute simple and robust message-passing schemes for distributed information processing over networks. However for many topologies that are realistic…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…
Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…
There exist many orthogonal graph drawing algorithms that minimize edge crossings or edge bends, however they produce unsatisfactory drawings in many practical cases. In this paper we present a grid-based algorithm for drawing orthogonal…
The goal of this paper is to propose novel strategies for adaptive learning of signals defined over graphs, which are observed over a (randomly time-varying) subset of vertices. We recast two classical adaptive algorithms in the graph…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size…
Due to the computational complexity of finding almost shortest simple paths, we propose that identifying a larger collection of (nonbacktracking) paths is more efficient than finding almost shortest simple paths on positively weighted…