Related papers: Constrained Routing Between Non-Visible Vertices
The directed graph reachability problem takes as input an $n$-vertex directed graph $G=(V,E)$, and two distinguished vertices $s$ and $t$. The problem is to determine whether there exists a path from $s$ to $t$ in $G$. This is a canonical…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
The Vehicle Routing Problem is about optimizing the routes of vehicles to meet the needs of customers at specific locations. The route graph consists of depots on several levels and customer positions. Several optimization methods have been…
Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the…
We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2022). In this problem, an agent, starting at some vertex $r$ has to traverse a (potentially unknown) graph $G$ to find a hidden goal node…
The packet routing problem asks to select routing paths that minimize the maximum edge congestion for a set of packets specified by source-destination vertex pairs. We revisit a semi-oblivious approach to this problem: each…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…
Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
Hybrid networks, i.e., networks that leverage different means of communication, become ever more widespread. To allow theoretical study of such networks, [Augustine et al., SODA'20] introduced the $\mathsf{HYBRID}$ model, which is based on…
We present a deterministic local routing algorithm that is guaranteed to find a path between any pair of vertices in a half-$\theta_6$-graph (the half-$\theta_6$-graph is equivalent to the Delaunay triangulation where the empty region is an…
We describe an efficient method for drawing any n-vertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed…
In a directed graph $G=(V,E)$ with a capacity on every edge, a \emph{bottleneck path} (or \emph{widest path}) between two vertices is a path maximizing the minimum capacity of edges in the path. For the single-source all-destination version…
Graph drawing addresses the problem of finding a layout of a graph that satisfies given aesthetic and understandability objectives. The most important objective in graph drawing is minimization of the number of crossings in the drawing, as…
Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with…
In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent…
We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…