Related papers: Minimum firing times of firing squad synchronizati…
We prove nonexistence of minimal-time solutions for three variations of the firing squad synchronization problem (FSSP, for short). Configurations of these variations are paths in the two-dimensional grid space having simple geometric…
We present different classes of solutions to the Firing Squad Synchronization Problem on networks of different shapes. The nodes are finite state processors that work at unison discrete steps. The networks considered are the line, the ring…
The firing squad synchronization problem (FSSP, for short) is a problem in automata theory introduced in 1957 by John Myhill. Its goal is to design a finite automaton A such that, if copies of A are placed in a line and connected and are…
We solve the Firing Squad Synchronization Problem (FSSP), for P systems based on digraphs with simplex channels, where communication is restricted by the direction of structural arcs. Previous work on FSSP for P systems focused exclusively…
We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is…
We study the problem of simultaneous geometric embedding of two paths without self-intersections on an integer grid. We show that minimizing the length of the longest edge of such an embedding is NP-hard. We also show that we can minimize…
Consider a fully-connected synchronous distributed system consisting of $n$ nodes, where up to $f$ nodes may be faulty and every node starts in an arbitrary initial state. In the synchronous $C$-counting problem, all nodes need to…
Given starting and ending positions and velocities, $L_2$ bounds on the acceleration and velocity, and the restriction to no more than two constant control inputs, this paper provides routines to compute the minimal-time path. Closed form…
In a static spacetime, the Killing time can be used to measure the time required for signals or objects to propagate between two of its orbits. By further restricting to spherically symmetric cases, one obtains a natural association between…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
Through the Pontryagin maximum principle, we solve a minimal-time problem for a linear control system on a cylinder, considered as a homogeneous space of the solvable Lie group of dimension two. The main result explicitly shows the…
We investigate the problem of finding paths that enable a robot modeled as a Dubins car (i.e., a constant-speed finite-turn-rate unicycle) to escape from a circular region of space in minimum time. This minimum-time escape problem arises in…
We study the multi-agent path finding problem (MAPF) for a group of agents which are allowed to move into arbitrary directions on a 2D square grid. We focus on centralized conflict resolution for independently computed plans. We propose an…
In this paper, we solve the local gathering problem of a swarm of $n$ indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time $\mathcal{O}(n)$ in the fully synchronous $\mathcal{FSYNC}$ time model.…
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
Consider a fully connected network where up to $t$ processes may crash, and all processes start in an arbitrary memory state. The self-stabilizing firing squad problem consists of eventually guaranteeing simultaneous response to an external…
Firefighting is a complex, yet low automated task. To mitigate ergonomic and safety related risks on the human operators, robots could be deployed in a collaborative approach. To allow human-robot teams in firefighting, important basics are…
The solving of least square systems is a useful operation in neurocomputational modeling of learning, pattern matching, and pattern recognition. In these last two cases, the solution must be obtained on-line, thus the time required to solve…
An autonomous robot with a limited vision range finds a path to the goal in an unknown environment in 2D avoiding polygonal obstacles. In the process of discovering the environmental map, the robot has to return to some positions marked…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…