Related papers: Interval Routing Schemes for Circular-Arc Graphs
The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and…
We develop an efficient parallel algorithm for answering shortest-path queries in planar graphs and implement it on a multi-node CPU/GPU clusters. The algorithm uses a divide-and-conquer approach for decomposing the input graph into small…
Dedicated short-range communication (DSRC) enables vehicular communication using periodic broadcast messages. We propose to use these periodic broadcasts to perform inter-vehicle ranging. Motivated by this scenario, we study the general…
This paper studies the fundamental problem of how to reroute $k$ unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast. This scheduling…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
We study the problem of enumerating the $k$-arc-connected orientations of a graph $G$, i.e., generating each exactly once. A first algorithm using submodular flow optimization is easy to state, but intricate to implement. In a second…
This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous…
We investigate a scheduling scheme incorporating network coding and channel varying information for the two-way relay networks. Our scheduler aims at minimizing the time span needed to send all the data of each source of the network. We…
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
Motivated by an emerging framework of Autonomous Modular Vehicles, we consider the abstract problem of optimally routing two modules, i.e., vehicles that can attach to or detach from each other in motion on a graph. The modules' objective…
Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…
We study $c$-crossing-critical graphs, which are the minimal graphs that require at least $c$ edge-crossings when drawn in the plane. For $c=1$ there are only two such graphs without degree-2 vertices, $K_5$ and $K_{3,3}$, but for any fixed…
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…
The shortest-path distance is a fundamental concept in graph analytics and has been extensively studied in the literature. In many real-world applications, quality constraints are naturally associated with edges in the graphs and finding…
In this article we present an efficient algorithm to compute rotation intervals of circle maps of degree one. It is based on the computation of the rotation number of a monotone circle map of degree one with a constant section. The main…
We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. We show that it is NP-complete to decide whether a graph has an orientation such that…
Although there are very algorithms for embedding graphs on unbounded grids, only few results on embedding or drawing graphs on restricted grids has been published. In this work, we consider the problem of embedding paths and cycles on grid…
A mixed graph has a set of vertices, a set of undirected egdes, and a set of directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that assigns to each vertex in $G$ a positive integer such that, for each edge $uv$ in $G$,…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Platooning of vehicles is a promising approach for reducing fuel consumption, increasing vehicle safety, and using road space more efficiently. We consider the important but difficult problem of assigning optimal routes and departure…