Rendezvous of Heterogeneous Mobile Agents in Edge-weighted Networks

We introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal times for the other agent. The goal of the agents is to meet on an edge or a node of the graph. In this scenario, we study the time required by the agents to meet, compared to the meeting time $T_{OPT}$ in the offline scenario in which the agents have complete knowledge about each others speed characteristics. When no additional assumptions are made, we show that rendezvous in our model can be achieved after time $O(n T_{OPT})$ in a $n$-node graph, and that such time is essentially in some cases the best possible. However, we prove that the rendezvous time can be reduced to $\Theta (T_{OPT})$ when the agents are allowed to exchange $\Theta(n)$ bits of information at the start of the rendezvous process. We then show that under some natural assumption about the traversal times of edges, the hardness of the heterogeneous rendezvous problem can be substantially decreased, both in terms of time required for rendezvous without communication, and the communication complexity of achieving rendezvous in time $\Theta (T_{OPT})$

Deterministic Symmetry Breaking in Ring Networks

We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronised rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that $n$ mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The {\em location discovery} task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to %information about distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201

Pattern formation with voluminous processes

When a shoal of small fishes notices a predator, they typically change their collective shape and form a specific pattern. They do so efficiently (in parallel) and without collision. This motivates us to design algorithms with similar properties. In this paper, we study the problem of distributed pattern formation. A set of processes needs to move from a set of initial positions to a set of final positions. The processes are oblivious (no internal memory) and must preserve, at any time, a minimal distance between them. A naive solution would be to move the processes one by one, but this would have a poor time complexity. The difficulty here is to move the processes simultaneously in clearly delimited phases (as there is no internal memory), no matter how unfavorable the initial configuration may be. We solve this by treating the problem ``dimension by dimension'': the processes first form 1D trails, then gather into a 2D shape (this technique can be generalized to higher dimensions). We present an optimal algorithm which time complexity depends linearly on the radius of the smallest circle containing both initial and final positions. The algorithm is self-stabilizing, as the processes are oblivious and the initial positions are arbitrary

Localization for a system of colliding robots

We study the localization problem in the ring: a collection of $$n$$n anonymous mobile robots are deployed in a continuous ring of perimeter one. All robots start moving at the same time with arbitrary velocities, starting in clockwise or counterclockwise direction around the ring. The robots bounce against each other according to the principles of conservation of energy and momentum. The task of each robot is to find out, in finite time, the initial position and the initial velocity of every deployed robot. The only way that robots perceive the information about the environment is by colliding with their neighbors; robots have no control of their wal

Localization for a system of colliding robots

We study the localization problem in the ring: a collection of n anonymous mobile robots are deployed in a continuous ring of perimeter one. All robots start moving at the same time along the ring with arbitrary velocity, starting in clockwise or counterclockwise direction around the ring. The robots bounce against each other when they meet. The task of each robot is to find out, in finite time, the initial position and the initial velocity of every deployed robot. The only way that robots perceive the information about the environment is by colliding with their neighbors; any type of communication among robots is not possible. We assume the principle of momentum conservation as well as the conservation of energy, so robots exchange velocities when they collide. The capabilities of each robot are limited to: observing