Showing papers by "Evangelos Kranakis published in 2020"

Capacity Requirements in Networks of Quantum Repeaters and Terminals

Abstract: We consider the problem of path congestion avoidance in networks of quantum repeaters and terminals. In other words, the avoidance of situations when demands exceed capacity. We assume networks in which the sets of complete paths between terminals may affect the capacity of repeaters in the network. We compare the reduction of congestion avoidance of two representative path establishment algorithms: shortest-path establishment vs. layer-peeling path establishment. We observe that both strategies provide an equivalent entanglement rate, while the layer-peeling establishment algorithm considerably reduces the congestion in the network of repeaters. Repeaters in the inner layers get less congested and require a lower number of qubits, while providing a similar entanglement rate.

Weak Coverage of a Rectangular Barrier

Abstract: Assume n wireless mobile sensors are initially dispersed in an ad hoc manner in a rectangular region. They are required to move to final locations so that they can detect any intruder crossing the region in a direction parallel to the sides of the rectangle, and thus provide weak barrier coverage of the region. We study three optimization problems related to the movement of sensors to achieve weak barrier coverage: minimizing the number of sensors moved (MinNum), minimizing the average distance moved by the sensors (MinSum), and minimizing the maximum distance moved by the sensors (MinMax). We give an \(O(n^{3/2})\) time algorithm for the MinNum problem for sensors of diameter 1 that are initially placed at integer positions; in contrast we show that the problem is NP-hard even for sensors of diameter 2 that are initially placed at integer positions. We show that the MinSum problem is solvable in \(O(n \log n)\) time for homogeneous range sensors in arbitrary initial positions for the Manhattan metric, while it is NP-hard for heterogeneous sensor ranges for both Manhattan and Euclidean metrics. Finally, we prove that even very restricted homogeneous versions of the MinMax problem are NP-hard.

Geocaching-Inspired Navigation for Micro Aerial Vehicles with Fallible Place Recognition

Abstract: This paper extends an existing decisional framework for the navigation of Micro Aerial Vehicle (MAV) swarms. The work finds inspiration in the geocaching outdoor game. It leverages place recognition methods, information sharing and collaborative work between MAVs. It is unique in that a priori none of the MAVs knows the trajectory, waypoints and destination. The MAVs collectively solve a series of problems that involve the recognition of physical places and determination of their GPS coordinates. Our algorithm builds upon various methods that had been created for place recognition. The need for a decisional framework comes from the fact that all methods are fallible and make place recognition errors. In this paper, we augment the navigation algorithm with a decisional framework resolving conflicts resulting from errors made by place recognition methods. The errors divide the members of a swarm with respect to the location of waypoints (i.e., some members continue the trip following the proper itinary; others follow a wrong one). We propose four decisional algorithms to resolve conflicts among members of a swarm due to place recognition errors. The performance of the decisional algorithms is modeled and analyzed.

Minimizing The Maximum Distance Traveled To Form Patterns With Systems of Mobile Robots

Abstract: In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection In other words, a valid final configuration of the system is a formation that is \textit{similar} to the desired pattern While there has been no shortage of research in the pattern formation problem under a variety of assumptions, models, and contexts, we consider the additional constraint that the maximum distance traveled among all robots in the system is minimum Existing work in pattern formation and closely related problems are typically application-specific or not concerned with optimality (but rather feasibility) We show the necessary conditions any optimal solution must satisfy and present a solution for systems of three robots Our work also led to an interesting result that has applications beyond pattern formation Namely, a metric for comparing two triangles where a distance of $0$ indicates the triangles are similar, and $1$ indicates they are \emph{fully dissimilar}

Plane and planarity thresholds for random geometric graphs

Abstract: A random geometric graph, G(n,r), is formed by choosing n points independently and uniformly at random in a unit square; two points are connected by a straight-line edge if they are at Euclidean distance at most r. For a given constant k, we show that n -k 2k-2 is a distance threshold function for G(n,r) to have a connected subgraph on k points. Based on this, we show that n-2/3 is a distance threshold for G(n,r) to be plane, and n-5/8 is a distance threshold to be planar. We also investigate distance thresholds for G(n,r) to have a non-crossing edge, a clique of a given size, and an independent set of a given size.

The Bike Sharing Problem.

Abstract: Assume that $m \geq 1$ autonomous mobile agents and $0 \leq b \leq m$ single-agent transportation devices (called {\em bikes}) are initially placed at the left endpoint $0$ of the unit interval $[0,1]$ The agents are identical in capability and can move at speed one The bikes cannot move on their own, but any agent riding bike $i$ can move at speed $v_i > 1$ An agent may ride at most one bike at a time The agents can cooperate by sharing the bikes; an agent can ride a bike for a time, then drop it to be used by another agent, and possibly switch to a different bike We study two problems In the \BS problem, we require all agents and bikes starting at the left endpoint of the interval to reach the end of the interval as soon as possible In the \RBS problem, we aim to minimize the arrival time of the agents; the bikes can be used to increase the average speed of the agents, but are not required to reach the end of the interval Our main result is the construction of a polynomial time algorithm for the \BS problem that creates an arrival-time optimal schedule for travellers and bikes to travel across the interval For the \RBS problem, we give an algorithm that gives an optimal solution for the case when at most one of the bikes can be abandoned