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Autonomous identical robots represented by unit discs move deterministically in the plane. They do not have any common coordinate system, do not communicate, do not have memory of the past and are totally asynchronous. Gathering such robots means forming a configuration for which the union of all discs representing them is connected. We solve the gathering(More)
Two mobile agents (robots) with distinct labels have to meet in an arbitrary, possibly infinite, unknown connected graph or in an unknown connected terrain in the plane. Agents are modeled as points, and the route of each of them only depends on its label and on the unknown environment. The actual walk of each agent also depends on an asynchronous adversary(More)
Simultaneous diagonal flips in plane triangulations are investigated. It is proved that every triangulation with at least six vertices has a simultaneous flip into a 4-connected triangulation, and that it can be computed in linear time. It follows that every triangulation has a simultaneous flip into a Hamiltonian triangulation. This result is used to prove(More)
Let shape P be any simply-connected set in the plane, bounded by a Jordan curve, that is not a circular disk. We say that a set of points I on the boundary of P immobilize the shape if any rigid motion of P in the plane causes at least one point of I to penetrate the interior of P. We prove that four points always suffice to immobilize any shape. For a(More)
We consider n mobile sensors located on a line containing a barrier represented by a finite line segment. Sensors form a wireless sensor network and are able to move within the line. An intruder traversing the barrier can be detected only when it is within the sensing range of at least one sensor. The sensor network establishes barrier coverage of the(More)
A set of k mobile agents are placed on the boundary of a simply connected planar object represented by a cycle of unit length. Each agent has its own predefined maximal speed, and is capable of moving around this boundary without exceeding its maximal speed. The agents are required to protect the boundary from an intruder which attempts to penetrate to the(More)
We consider the problem of cooperative network exploration by agents under the assumption that there is a harmful host present in the network that destroys the incoming agents without outside trace – the so-called black hole search problem. Many variants of this problem have been studied, with various assumptions about the timing, agents' knowledge about(More)
Many protocols in distributed computing make use of dominating and connected dominating sets, for example for broadcasting and the computation of routing. Ad hoc networks impose an additional requirement that algorithms for the construction of such sets should be local in the sense that each node of the network should make decisions based only on the(More)
Consider a DAG (directed acyclic graph) G = (V; E) representing a collection V of web pages connected via links E. All web pages can be reached from a designated source page, represented by a source node s of G. Each web page carries a weight representative of the frequency with which it is visited. By adding hotlinks, at most one per page, we are(More)