Competitive Local Routing with Constraints

Let $P$ be a set of $n$ vertices in the plane and $S$ a set of non-crossing line segments between vertices in $P$, called constraints. Two vertices are visible if the straight line segment connecting them does not properly intersect any constraints. The constrained $\Theta_m$-graph is constructed by partitioning the plane around each vertex into $m$ disjoint cones, each with aperture $\theta = 2 \pi/m$, and adding an edge to the `closest' visible vertex in each cone. We consider how to route on the constrained $\Theta_6$-graph. We first show that no deterministic 1-local routing algorithm is $o(\sqrt{n})$-competitive on all pairs of vertices of the constrained $\Theta_6$-graph. After that, we show how to route between any two visible vertices of the constrained $\Theta_6$-graph using only 1-local information. Our routing algorithm guarantees that the returned path is 2-competitive. Additionally, we provide a 1-local 18-competitive routing algorithm for visible vertices in the constrained half-$\Theta_6$-graph, a subgraph of the constrained $\Theta_6$-graph that is equivalent to the Delaunay graph where the empty region is an equilateral triangle. To the best of our knowledge, these are the first local routing algorithms in the constrained setting with guarantees on the length of the returned path

Routing on the Visibility Graph

We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of non-crossing line segments whose endpoints are in $P$. We present two deterministic 1-local $O(1)$-memory routing algorithms that are guaranteed to find a path of at most linear size between any pair of vertices of the \emph{visibility graph} of $P$ with respect to a set of constraints $S$ (i.e., the algorithms never look beyond the direct neighbours of the current location and store only a constant amount of additional information). Contrary to {\em all} existing deterministic local routing algorithms, our routing algorithms do not route on a plane subgraph of the visibility graph. Additionally, we provide lower bounds on the routing ratio of any deterministic local routing algorithm on the visibility graph.Comment: An extended abstract of this paper appeared in the proceedings of the 28th International Symposium on Algorithms and Computation (ISAAC 2017). Final version appeared in the Journal of Computational Geometr

A Lagrangian approach to Chance Constrained Routing with Local Broadcast

Mobile cellular networks play a pivotal role in emerging Internet of Things (IoT) applications, such as vehicular collision alerts, malfunctioning alerts in Industry-4.0 manufacturing plants, periodic distribution of coordination information for swarming robots or platooning vehicles, etc. All these applications are characterized by the need of routing messages within a given local area (geographic proximity) with constraints about both timeliness and reliability (i.e., probability of reception). This paper presents a Non-Convex Mixed-Integer Nonlinear Programming model for a routing problem with probabilistic constraints on a wireless network. We propose an exact approach consisting of a branch-and-bound framework based on a novel Lagrangian decomposition to derive lower bounds. Preliminary experimental results indicate that the proposed algorithm is competitive with state-of-the-art general-purpose solvers, and can provide better solutions than existing highly tailored ad-hoc heuristics to this problem

On resilient control of dynamical flow networks

Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the recent technological advancements. The problem has motivated a considerable amount of research within the last few years, particularly focused on the dynamical aspects of network flows, complementing more classical static network flow optimization approaches. In this tutorial paper, a class of single-commodity first-order models of dynamical flow networks is considered. A few results recently appeared in the literature and dealing with stability and robustness of dynamical flow networks are gathered and originally presented in a unified framework. In particular, (differential) stability properties of monotone dynamical flow networks are treated in some detail, and the notion of margin of resilience is introduced as a quantitative measure of their robustness. While emphasizing methodological aspects -- including structural properties, such as monotonicity, that enable tractability and scalability -- over the specific applications, connections to well-established road traffic flow models are made.Comment: accepted for publication in Annual Reviews in Control, 201

Combined Coverage Area Reporting and Geographical Routing in Wireless Sensor-Actuator Networks for Cooperating with Unmanned Aerial Vehicles

In wireless sensor network (WSN) applications with multiple gateways, it is key to route location dependent subscriptions efficiently at two levels in the system. At the gateway level, data sinks must not waste the energy of the WSN by injecting subscriptions that are not relevant for the nodes in their coverage area and at WSN level, energy-efficient delivery of subscriptions to target areas is required. In this paper, we propose a mechanism in which (1) the WSN provides an accurate and up-to-date coverage area description to gateways and (2) the wireless sensor network re-uses the collected coverage area information to enable efficient geographical routing of location dependent subscriptions and other messages. The latter has a focus on routing of messages injected from sink nodes to nodes in the region of interest. Our proposed mechanisms are evaluated in simulation