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We present a general and intuitive ambiguity model for intersections, junctions and other structures in binary edge images. The model is combined with edge tracing, where edges are ordered sequences of connected pixels. The objective is to…
We revisit the complexity of online computation in the cell probe model. We consider a class of problems where we are first given a fixed pattern or vector $F$ of $n$ symbols and then one symbol arrives at a time in a stream. After each…
In trying to emulate the spatial position of wireless nodes for purpose of analysis, we rely on stochastic simulation. And, it is customary, for mobile systems, to consider a base-station radiation coverage by an ideal cell shape. For…
This article considers two variants of a shortest path problem for a car-like robot visiting a set of waypoints. The sequence of waypoints to be visited is specified in the first variant while the robot is allowed to visit the waypoints in…
We investigate the terminating grid exploration for autonomous myopic luminous robots. Myopic robots mean that they can observe nodes only within a certain fixed distance, and luminous robots mean that they have light devices that can emit…
Using mobile robots for autonomous patrolling of environments to prevent intrusions is a topic of increasing practical relevance. One of the most challenging scientific issues is the problem of finding effective patrolling strategies that,…
We present a method for solving the coverage problem with the objective of autonomously exploring an unknown environment under mission time constraints. Here, the robot is tasked with planning a path over a horizon such that the accumulated…
We consider the problem of completely covering an unknown discrete environment with a swarm of asynchronous, frequently-crashing autonomous mobile robots. We represent the environment by a discrete graph, and task the robots with occupying…
It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all one-dimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is…
The reachability problem asks to decide if there exists a path from one vertex to another in a digraph. In a grid digraph, the vertices are the points of a two-dimensional square grid, and an edge can occur between a vertex and its…
The dynamic problem of enclosing an expanding fire can be modelled by a discrete variant in a grid graph. While the fire expands to all neighbouring cells in any time step, the fire fighter is allowed to block $c$ cells in the average…
Robotic exploration of underground environments is a particularly challenging problem due to communication, endurance, and traversability constraints which necessitate high degrees of autonomy and agility. These challenges are further…
This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…
Recent literature in the robotics community has focused on learning robot behaviors that abstract out lower-level details of robot control. To fully leverage the efficacy of such behaviors, it is necessary to select and sequence them to…
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…
We present algorithms for uniformly covering an unknown indoor region with a swarm of simple, anonymous and autonomous mobile agents. The exploration of such regions is made difficult by the lack of a common global reference frame, severe…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of $n$ indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid…
We consider the problem of designing succinct navigational oracles, i.e., succinct data structures supporting basic navigational queries such as degree, adjacency, and neighborhood efficiently for intersection graphs on a circle, which…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…