arXiv subjects

Giovanni Viglietta

Publications and source records attributed to Giovanni Viglietta.

41 records · Page 3Linked to original sources

arXiv2012

Rendezvous of two robots with visible bits

We study the rendezvous problem for two robots moving in the plane (or on a line). Robots are autonomous, anonymous, oblivious, and carry colored lights that are visible to both. We consider deterministic distributed algorithms in which robots do not use distance information, but try to reduce (or increase) their distance by a constant factor, depending on their lights' colors. We give a complete characterization of the number of colors that are necessary to solve the rendezvous problem in every possible model, ranging from fully synchronous to semi-synchronous to asynchronous, rigid and non-rigid, with preset or arbitrary initial configuration. In particular, we show that three colors are sufficient in the non-rigid asynchronous model with arbitrary initial configuration. In contrast, two colors are insufficient in the rigid asynchronous model with arbitrary initial configuration and in the non-rigid asynchronous model with preset initial configuration. Additionally, if the robots are able to distinguish between zero and non-zero distances, we show how they can solve rendezvous and detect termination using only three colors, even in the non-rigid asynchronous model with arbitrary initial configuration.

cs.MA↗

arXiv2012

Guarding and Searching Polyhedra

We tackle the Art Gallery Problem and the Searchlight Scheduling Problem in 3-dimensional polyhedral environments, putting special emphasis on edge guards and orthogonal polyhedra.

cs.CG↗

arXiv2012

Hardness of Mastermind

Mastermind is a popular board game released in 1971, where a codemaker chooses a secret pattern of colored pegs, and a codebreaker has to guess it in several trials. After each attempt, the codebreaker gets a response from the codemaker containing some information on the number of correctly guessed pegs. The search space is thus reduced at each turn, and the game continues until the codebreaker is able to find the correct code, or runs out of trials. In this paper we study several variations of #MSP, the problem of computing the size of the search space resulting from a given (possibly fictitious) sequence of guesses and responses. Our main contribution is a proof of the #P-completeness of #MSP under parsimonious reductions, which settles an open problem posed by Stuckman and Zhang in 2005, concerning the complexity of deciding if the secret code is uniquely determined by the previous guesses and responses. Similarly, #MSP stays #P-complete under Turing reductions even with the promise that the search space has at least k elements, for any constant k. (In a regular game of Mastermind, k=1.) All our hardness results hold even in the most restrictive setting, in which there are only two available peg colors, and also if the codemaker's responses contain less information, for instance like in the so-called single-count (black peg) Mastermind variation.

cs.GT↗

arXiv2011

Searching Polyhedra by Rotating Half-Planes

The Searchlight Scheduling Problem was first studied in 2D polygons, where the goal is for point guards in fixed positions to rotate searchlights to catch an evasive intruder. Here the problem is extended to 3D polyhedra, with the guards now boundary segments who rotate half-planes of illumination. After carefully detailing the 3D model, several results are established. The first is a nearly direct extension of the planar one-way sweep strategy using what we call exhaustive guards, a generalization that succeeds despite there being no well-defined notion in 3D of planar "clockwise rotation". Next follow two results: every polyhedron with r>0 reflex edges can be searched by at most r^2 suitably placed guards, whereas just r guards suffice if the polyhedron is orthogonal. (Minimizing the number of guards to search a given polyhedron is easily seen to be NP-hard.) Finally we show that deciding whether a given set of guards has a successful search schedule is strongly NP-hard, and that deciding if a given target area is searchable at all is strongly PSPACE-hard, even for orthogonal polyhedra. A number of peripheral results are proved en route to these central theorems, and several open problems remain for future work.

cs.CG↗

arXiv2011

A Survey on Open Problems for Mobile Robots

Gathering mobile robots is a widely studied problem in robotic research. This survey first introduces the related work, summarizing models and results. Then, the focus shifts on the open problem of gathering fat robots. In this context, "fat" means that the robot is not represented by a point in a bidimensional space, but it has an extent. Moreover, it can be opaque in the sense that other robots cannot "see through" it. All these issues lead to a redefinition of the original problem and an extension of the CORDA model. For at most 4 robots an algorithm is provided in the literature, but is gathering always possible for n>4 fat robots? Another open problem is considered: Boundary Patrolling by mobile robots. A set of mobile robots with constraints only on speed and visibility is working in a polygonal environment having boundary and possibly obstacles. The robots have to perform a perpetual movement (possibly within the environment) so that the maximum timespan in which a point of the boundary is not being watched by any robot is minimized.

cs.RO↗