Giovanni Viglietta

Japan Advanced Institute of Science and Technology

A network is said to be "anonymous" if its agents are indistinguishable from each other; it is "dynamic" if its communication links may appear or disappear unpredictably over time. Assuming that an anonymous dynamic network is always connected and each of its $n$ agents is initially given an input, it takes $2n$ communication rounds for the agents...

We prove that, given a polyhedron \({\mathcal {P}}\) in \({\mathbb {R}}^3\), every point in \({\mathbb {R}}^3\) that does not see any vertex of \({\mathcal {P}}\) must see eight or more edges of \({\mathcal {P}}\), and this bound is tight. More generally, this remains true if \({\mathcal {P}}\) is any finite arrangement of internally disjoint polyg...

An "anonymous dynamic network" is a network of indistinguishable processes whose communication links may appear or disappear unpredictably over time. Previous research has shown that deterministically computing an arbitrary function of a multiset of input values given to these processes takes only a linear number of communication rounds. However, f...

We investigate a new variation of a token reconfiguration problem on graphs using the cyclic shift operation. A colored or labeled token is placed on each vertex of a given graph, and a “move” consists in choosing a cycle in the graph and shifting tokens by one position along its edges. Given a target arrangement of tokens on the graph, our goal is...

We give a simple and complete characterization of which functions can be deterministically computed by anonymous processes in disconnected dynamic networks, depending on the number of leaders in the network. In addition, we provide efficient distributed algorithms for computing all such functions assuming minimal or no knowledge about the network....

We give the first linear-time counting algorithm for processes in anonymous 1-interval-connected dynamic networks with a leader. As a byproduct, we are able to compute in $3n$ rounds every function that is computable deterministically in such networks. If explicit termination is not required, the running time improves to $2n$ rounds, which we show...

In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Each robot is punctiform and memoryless, it operates in $\mathbb{R}^m$, it has a local referen...

We study the computational complexity of the puzzle game Critter Crunch, where the player has to rearrange Critters on a board in order to eliminate them all. Smaller Critters can be fed to larger Critters, and Critters will explode if they eat too much. Critters come in several different types, sizes, and colors. We prove the NP-hardness of levels...

In this paper, we introduce a path embedding problem inspired by the well-known hydrophobic-polar (HP) model of protein folding. A graph is said bicolored if each vertex is assigned a label in the set {red, blue}. For a given bicolored path P and a given bicolored graph G, our problem asks whether we can embed P into G in such a way as to match the...

We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the tokens from a given initial configuration to a final one by using cyclic shift operations along the distinguished c...

We introduce the axiomatic theory of Spherical Occlusion Diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context Art Gallery problems for polyhedra and other visibility-related problems in discrete and computational geometry.

We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others' work on beacon-based routing. Consider a human and a puppy on a simple closed curve in the plane. The human can walk along the curve at bounded speed and change direction as desired. The puppy runs with unbounded speed along the curve as long as the Euc...

We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the tokens from a given initial configuration to a final one by using cyclic shift operations along the distinguished c...

In this paper we investigate the computational power of population protocols under some unreliable or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of po...

The \emph{Meeting problem} for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its...

We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the tokens from a given initial configuration to a final one by using cyclic shift operations along the distinguished c...

In the distributed model Amoebot of programmable matter, the computational entities, called particles, are anonymous finite-state machines that operate and move on a hexagonal tessellation of the plane. In this paper we show how a constant number of such weak particles can simulate a powerful Turing-complete entity that is able to move on the plane...

A swarm of anonymous oblivious mobile robots, operating in deterministic Look-Compute-Move cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial semi-synchronous scheduler (SSYNCH), and an active robot always reaches the destination point it computes (rigidity). Ro...

We investigate computational issues in the distributed model Amoebots of programmable matter. In this model, the computational entities, called particles, are anonymous finite-state machines that operate and move on an hexagonal tasselation of the plane. In this paper we show how a constant number of such weak particles can simulate a powerful Turi...

Shape formation is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexa...

We consider a distributed system of n identical mobile robots operating in the two dimensional Euclidian plane. As in the previous studies, we consider the robots to be anonymous, oblivious, dis-oriented, and without any communication capabilities, operating based on the Look-Compute-Move model where the next location of a robot depends only on its...

The classic Look-Compute-Move model of oblivious robots has many strengths: algorithms designed for this model are inherently resistant to a large set of failures that can affect the memory of the robots and their communication capabilities.

We treat the second of the two patterns that are formable in the \(\mathcal{OBLOT}\) model from every initial configuration of n robots: Uniform Circle, i.e., the pattern where the robots are located at the vertices of a regular n-gon. The algorithm presented in this chapter solves the Uniform Circle Formation Problem in the standard \(\mathcal{OBL...

The gathering (or multi-agent rendezvous) problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during...

We consider the problem of simulating traditional population protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner's state during an interaction), which in turn may be detectable or undetectable. We focus on the impac...

Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when f of the n particles have crashed. We focus on the basic line shape, used as a tool for the construction of more complex configurations. We present a solution to the line recove...

The gathering (or multi-agent rendezvous) problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced.

Consider a set of n finite set of simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study the...

We study the problem of guarding an orthogonal polyhedron having reflex edges in just two directions (as opposed to three) by placing guards on reflex edges only. We show that (r - g)/2 + 1 reflex edge guards are sufficient, where r is the number of reflex edges in a given polyhedron and g is its genus. This bound is tight for g=0. We thereby gener...

Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when $f$ of the $n$ particles have crashed. We focus on the basic line shape, used as a tool for the construction of more complex configurations. We present a solution to the line re...

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of the network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption that the topological structure does not change during the rendezvous or the...

We consider the problem of simulating traditional population protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner’s state during an interaction), which in turn may be detectable or undetectable. We focus on the impac...

Mediated population protocols are an extension of population protocols in which communication links, as well as agents, have internal states. We study the leader election problem and some applications in constant-state mediated population protocols. Depending on the power of the adversarial scheduler, our algorithms are either stabilizing or allow...

Population protocols (PPs) are used as a model for a collection of finite-state mobile agents which interact with each other to accomplish a common task. Unlike most of the previous works, which investigate their computational power, this paper throws light on an aspect of PPs as a model of chemical reactions. Motivated by the well-known BZ reactio...

We consider the problem of simulating traditional population protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner's state during an interaction), which in turn may be detectable or undetectable. We focus on the impac...

In this paper we investigate the computational power of Population Protocols (PP) under some unreliable and/or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the cont...

An oblivious mobile robot is a stateless computational entity located in a spatial universe, capable of moving in that universe. When activated, the robot observes the universe and the location of the other robots, chooses a destination, and moves there. The computation of the destination is made by executing an algorithm, the same for all robots,...

Mario is back! In this sequel, we prove that solving a generalized level of Super Mario Bros. is PSPACE-complete, strengthening the previous NP-hardness result (FUN 2014). Both our PSPACE-hardness and the previous NP-hardness use levels of arbitrary dimensions and require either arbitrarily large screens or a game engine that remembers the state of...

A fundamental problem in Distributed Computing is the Pattern Formation problem, where some independent mobile entities, called robots, have to rearrange themselves in such a way as to form a given figure from every possible (non-degenerate) initial configuration. In the present paper, we consider robots that operate in the Euclidean plane and are...

An oblivious mobile robot is a stateless computational entity located in a spatial universe, capable of moving in that universe. When activated, the robot observes the universe and the location of the other robots, chooses a destination, and moves there. The computation of the destination is made by executing an algorithm, the same for all robots,...

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has...

Population protocols (PPs) are a model of passive distributed systems in which a collection of finite-state mobile agents interact with each other to accomplish a common task. Unlike other works, which investigate their computation power, this paper throws light on an aspect of PPs as a model of chemical reactions. Motivated by the wellknown BZ rea...

A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three shadows of a cycle (i.e., a simple closed curve) in $\mathbb R^3$ to be paths (i.e., simple open curves). We also show two contrasting results: the three shadows of a pa...

We show how to simulate a roll of a fair $n$-sided die by one flip of a biased coin with probability $1/n$ of coming up heads, followed by $3\lfloor\log_2 n \rfloor+1$ flips of a fair coin.

In this paper we study the Near-Gathering problem for a finite set of dimensionless, deterministic, asynchronous, anonymous, oblivious and autonomous mobile robots with limited visibility moving in the Euclidean plane in Look-Compute-Move (LCM) cycles. In this problem, the robots have to get close enough to each other, so that every robot can see a...

Consider a finite set of identical computational entities that can move freely in the Euclidean plane operating in Look-Compute-Move cycles. Let p(t) denote the location of entity p at time t; entity p can see entity q at time t if at that time no other entity lies in the line segment p(t)q(t). We consider the basic problem called Mutual Visibility...

We prove NP-hardness results for five of Nintendo's largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to generalized versions of Super Mario Bros.1-3, The Lost Levels, and Super Mario World; Donkey Kong Country 1-3; all Legend of Zelda games; all Metroid games; and all Pokémon role-playing g...

We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on the external walls of a dark building, in order to completely illuminate its interior? We consider both closed and open face guards (i.e., faces with or without their boun...

Consider a set of $n\notin\{4,8\}$ simple autonomous mobile robots (decentralized, asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study...

We prove that every simple polygon can be made as a (2D) pop-up card/book that opens to any desired angle between 0 and 360°. More precisely, given a simple polygon attached to the two walls of the open pop-up, our polynomial-time algorithm subdivides the polygon into a single-degree-of-freedom linkage structure, such that closing the pop-up flatte...

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation...

Robots with lights is a model of autonomous mobile computational entties operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation o...

We establish some general schemes relating the computational complexity of a video game to the presence of certain common elements or mechanics, such as destroyable paths, collectible items, doors opened by keys or activated by buttons or pressure plates, etc. Then we apply such “metatheorems” to several video games published between 1980 and 1998,...

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities have no persistent memory, even if the system is semi-synchronous and movements are rigid. It has been r...

We study the Art Gallery Problem for face guards in polyhedral environments. The problem can be informally stated as: how many (not necessarily convex) windows should we place on the external walls of a dark building, in order to completely illuminate it? We consider both closed and open face guards (i.e., faces with or without their boundary), and...

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, depe...

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.

In this paper we study the Near-Gathering problem for a set of asynchronous, anonymous, oblivious and autonomous mobile robots with limited visibility moving in Look-Compute-Move (LCM) cycles: In this problem, the robots have to get close enough to each other, so that every robot can see all the others, without touching (i.e., colliding) with any o...

Lemmings is a computer puzzle game developed by DMA Design and published by Psygnosis in 1991, in which the player has to guide a tribe of lemming creatures to safety through a hazardous landscape, by assigning them specific skills that modify their behavior in different ways. In this paper we study the optimization problem of saving the highest nu...

We establish some general schemes relating the computational complexity of a video game to the presence of certain common elements or mechanics, such as destroyable paths, collectible items, doors opened by keys or activated by buttons or pressure plates, etc. Then we apply such "metatheorems" to several video games published between 1980 and 1998,...

The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of deciding if the polygon can be searched by a given set of guards is a long-standing open problem. Here we propo...

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 tur...

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...

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 re...

We address the question: How many edge guards are needed to guard an orthogonal polyhedron of e edges, r of which are reflex? It was previously established [3] that e/12 are sometimes necessary and e/6 always suffice. In contrast to the closed edge guardsused for these bounds, we introduce a new model, open edge guards (excluding the endpoints of t...

The problem of searching for a mobile intruder in a polygonal region by a set of stationary guards, each car- rying an orientable laser, is known in the literature as the Searchlight Scheduling Problem. A long-standing conjecture concerns the NP-hardness of deciding if a given polygon is searchable by a given set of guards. In this paper we introdu...