# Pedro MontealegreUniversité d'Orléans | UO · Département d'Informatique

Pedro Montealegre

## About

72

Publications

1,372

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303

Citations

Citations since 2017

Introduction

## Publications

Publications (72)

Naor, Parter, and Yogev [SODA 2020] recently designed a compiler for automatically translating standard centralized interactive protocols to distributed interactive protocols, as introduced by Kol, Oshman, and Saxena [PODC 2018]. In particular, by using this compiler, every linear-time algorithm for deciding the membership to some fixed graph class...

A Maximal Independent Set (MIS) is an inclusion maximal set of pairwise non-adjacent vertices. The computation of an MIS is one of the core problems in distributed computing. In this article, we introduce and analyze a finite-state distributed randomized algorithm for computing a Maximal Independent Set (MIS) on arbitrary undirected graphs. Our alg...

Consensus is an emergent property of many complex systems, considering this as an absolute majority phenomenon. In this work we study consensus dynamics in grids (in silicon), where individuals (the vertices) with two possible opinions (binary states) interact with the eight nearest neighbors (Moore’s neighborhood). Dynamics emerge once the majorit...

The density classification problem on graphs consists in finding a local dynamics such that, given a graph and an initial configuration of 0’s and 1’s assigned to the nodes of the graph, the dynamics converge to the fixed point configuration of all 1’s if the fraction of 1’s is greater than the critical density (typically 1/2) and, otherwise, it co...

A majority automata is a two-state cellular automata, where each cell updates its state according to the most represented state in its neighborhood. A question that naturally arises in the study of these dynamical systems asks whether there exists an efficient algorithm that can be implemented in order to compute the state configuration reached by...

During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant numb...

We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a block sequential update scheme. Furthermore, we show that the decision problem consisting in determine if a give...

Given an elementary cellular automaton (ECA) with local transition rule [Formula: see text], two different types of local transitions are identified: the ones in which a cell remains in its current state, called inactive transitions, and the ones in which the cell changes its current state, which are called active transitions. The number of active...

Consider a network where each node has one over two possible states, namely healthy or infected. Given an initial configuration, the network evolves in discrete time-steps picking uniformly at random a single node and updating its state according to the following rule: if the node is infected, it remains infected. If the node is healthy it switches...

A graph \(G=(V,E)\) is a geometric intersection graph if every node \(v \in V\) is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph classes have been studied from both the theoretical and practical point of view. On the one hand, many hard pro...

Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a
given boolean predicate. A certificate is assigned to each process in the system by a non-trustable oracle, and the processes are in charge of verifying these cert...

A graph $G=(V,E)$ is a geometric intersection graph if every node $v \in V$ is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph classes have been studied from both the theoretical and practical point of view. On the one hand, many hard problem...

Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate is assigned to each process in the system by a non-trustable oracle, and the processes are in charge of verifying these cert...

We present compact distributed interactive proofs for the recognition of two important graph classes, well-studied in the context of centralized algorithms, namely complement reducible graphs and distance-hereditary graphs. Complement reducible graphs (also called cographs) are defined as the graphs not containing a four-node path \(P_4\) as an ind...

We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a block sequential update scheme. Furthermore, we show that the decision problem consisting in determine if a give...

We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes are updated in parallel following a local totalistic rule, i.e., depending only on the sum of active states. F...

Naor M., Parter M., Yogev E.: (The power of distributed verifiers in interactive proofs. In: 31st ACM-SIAM symposium on discrete algorithms (SODA), pp 1096–115, 2020. https://doi.org/10.1137/1.9781611975994.67) have recently demonstrated the existence of a distributed interactive proof for planarity (i.e., for certifying that a network is planar),...

An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network’s graph. It is freezing if there is an order on states such that the state evolution of any node is non-decreasing in any orbit. They are commonly used to model epidemi...

In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to go from a lower to a higher state. A cellular automaton is asynchronous if at each time-step only one cell is u...

The NC versus P-hard classification of the prediction problem for sandpiles on the two dimensional grid with von Neumann neighborhood is a famous open problem. In this paper we make two kinds of progresses, by studying its freezing variant. First, it enables to establish strong connections with other well known prediction problems on networks of th...

We present compact distributed interactive proofs for the recognition of two important graph classes, well-studied in the context of centralized algorithms, namely complement reducible graphs and distance-hereditary graphs. Complement reducible graphs (also called cographs) are defined as the graphs not containing a four-node path $P_4$ as an induc...

We study the role of randomness in the broadcast congested clique model. This is a message-passing model of distributed computation where the nodes of a network know their local neighborhoods and they broadcast, in synchronous rounds, messages that are visible to every other node.
This works aims to separate three different settings: deterministic...

Naor, Parter, and Yogev [SODA 2020] recently designed a compiler for automatically translating standard centralized interactive protocols to distributed interactive protocols, as introduced by Kol, Oshman, and Saxena [PODC 2018]. In particular, by using this compiler, every linear-time algorithm for deciding the membership to some fixed graph class...

In distributed interactive proofs, the nodes of a graph G interact with a powerful but untrustable prover who tries to convince them, in a small number of rounds and through short messages, that G satisfies some property. This series of interactions is followed by a phase of distributed verification, which may be either deterministic or randomized,...

An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states such that the state evolution of any node is non-decreasing in any orbit. They are commonly used to model epidemi...

Naor, Parter, and Yogev (SODA 2020) have recently demonstrated the existence of a \emph{distributed interactive proof} for planarity (i.e., for certifying that a network is planar), using a sophisticated generic technique for constructing distributed IP protocols based on sequential IP protocols. The interactive proof for planarity is based on a di...

Given an elementary cellular automaton and a cell v, we define the stability decision problem as the determination of whether or not the state of cell v will ever change, at least once, during the time evolution of the rule, over a finite input configuration. Here, we perform the study of the entire elementary cellular automata rule space, for the...

Recent empirical findings suggest that societies have become more polarized in various countries. That is, the median voter of today represents a smaller fraction of society compared to two decades ago and yet, the mechanisms underlying this phenomenon are not fully understood. Since interactions between influential actors (“activists”) and voters...

We consider the asynchronous prediction problem for some automaton as the one consisting in determining, given an initial configuration, if there exists a non-zero probability that some selected site changes its state, when the network is updated picking one site at a time uniformly at random.
We show that for the majority automaton, the asynchrono...

In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbo...

In this paper we study the family of two-state Totalistic Freezing Cellular Automata (TFCA) defined over the triangular and square grids with von Neumann neighborhoods. We say that a Cellular Automaton is Freezing and Totalistic if the active cells remain unchanged, and the new value of an inactive cell depends only on the sum of its active neighbo...

In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to go from a lower to a higher state. A cellular automaton is asynchronous if at each time-step only one cell is u...

In a distributed locally-checkable proof, we are interested in checking the legality of a given network configuration with respect to some Boolean predicate. To do so, the network enlists the help of a prover—a computationally-unbounded oracle that aims at convincing the network that its state is legal, by providing the nodes with certificates that...

We introduce a restricted version of the Diffusion Limited Aggregation (DLA) model. DLA is a cluster growth model that consists in series of particles that are thrown one by one from the top edge of a two (on more) dimensional grid, where they undergo a random walk until they join the cluster. In our restricted version, particles are limited to mov...

Let \(\mathcal {P}(G,X)\) be a property associating a boolean value to each pair (G, X) where G is a graph and X is a vertex subset. Assume that \(\mathcal {P}\) is expressible in counting monadic second order logic (CMSO) and let t be an integer constant. We consider the following optimization problem: given an input graph \(G=(V,E)\), find subset...

Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel or \emph{synchronous} to \emph{asynchronous.} However, studying each possible dynamics defined by different upd...

In this paper we study the reconstruction problem in the congested clique model. In the reconstruction problem nodes are asked to recover all the edges of the input graph G. Formally, given a class of graphs \(\mathcal G\), the problem is defined as follows: if \(G \notin {\mathcal G}\), then every node must reject; on the other hand, if \(G \in {\...

In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper r-coloring φ of a graph G. We investigate the problem of finding a proper r-coloring of G, which is “the most similar” to φ, i.e., the number k of vertices that have to be recolored is minimum possible. We observe that the problem is...

Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within the traditional P vs NP dichotomy and within parameterized complexity. The \Pi-Subgraph problem asks whether...

We study the complexity of signed majority cellular automata on the planar grid. We show that, depending on their symmetry and uniformity, they can simulate different types of logical circuitry under different modes. We use this to establish new bounds on their overall complexity, concretely: the uniform asymmetric and the non-uniform symmetric rul...

In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is $\Omega(\mbox{poly}(n))$ rounds in $n$-node networks with constant diameter. Surprisingly, "local" tasks such as detecting the pres...

The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an $n$-node labeled graph $G$, i.e., the local input received by each node is the indicator function of its neig...

Consider a two dimensional lattice with the von Neumann neighborhood such that each site has a value belonging to \(\{0,1\}\) which changes state following a freezing non-strict majority rule, i.e., sites at state 1 remain unchanged and those at 0 change iff two or more of it neighbors are at state 1. We study the complexity of the decision problem...

In this paper we give upper bounds on the number of minimal separators and potential maximal cliques of graphs w.r.t. two graph parameters, namely vertex cover (\({\text {vc}}\)) and modular width (\({\text {mw}}\)). We prove that for any graph, the number of its minimal separators is \({\mathcal {O}}^*(3^{{\text {vc}}})\) and \({\mathcal {O}}^*(1....

Consider the robust prediction problem for some automaton as the one consisting in determine, given an initial configuration, if there exists a nonzero probability that some selected site change states, when the network is updated picking one site at a time uniformly at random. We show that the robust prediction is in NC for the two-dimensional, vo...

In many graph problems, like Longest Induced Path, Maximum Induced Forest, etc., we are given as input a graph G and the goal is to compute a largest induced subgraph G[F], of treewidth at most a constant t, and satisfying some property \(\mathcal {P}\). Fomin et al. [12] proved that this generic problem is polynomial on the class of graphs \({\mat...

We present deterministic constant-round protocols for the graph connectivity problem in the model where each of the n nodes of a graph receives a row of the adjacency matrix, and broadcasts a single sublinear size message to all other nodes. Communication rounds are synchronous. This model is sometimes called the broadcast congested clique. Specifi...

Fomin and Villanger (STACS 2010) proved that Maximum Independent Set, Feedback Vertex Set, and more generally the problem of finding a maximum induced subgraph of treewith at most a constant $t$, can be solved in polynomial time on graph classes with polynomially many minimal separators. We extend these results in two directions. Let $\Gpoly$ be th...

Fomin and Villanger ([14], STACS 2010) proved that Maximum Independent Set, Feedback Vertex Set, and more generally the problem of finding a maximum induced subgraph of treewith at most a constant t, can be solved in polynomial time on graph classes with polynomially many minimal separators. We extend these results in two directions. Let \(\mathcal...

In this paper we introduce automata networks to model some features of the emergence of a vocabulary related with the naming game model. We study the dynamical behaviour (attractors and convergence) of extremal and majority local functions.

We present a deterministic constant-round protocol for the graph connectivity problem in the model where each of the $n$ nodes of a graph receives a row of the adjacency matrix, and broadcasts a single sublinear size message to all other nodes. Communication rounds are synchronous. This model is sometimes called the broadcast congested clique. Spec...

We study the multiparty communication model where players are the nodes of a network and each of these players knows his/her own identifier together with the identifiers of his/her neighbors. The players simultaneously send a unique message to a referee who must decide a graph property. The goal of this article is to separate, from the point of vie...

We study the complexity of the majority rule on planar automata networks. We reduce a special case of the Monotone Circuit Value Problem to the prediction problem of determining if a vertex of a planar graph will change its state when the network is updated with the majority rule.

We study the dynamics of majority automata networks when the vertices are
updated according to a block sequential updating scheme. In particular, we show
that the complexity of the problem of predicting an eventual state change in
some vertex, given an initial configuration, is PSPACE-complete.

Given a threshold automata network, as well as an updating scheme over its vertices, we study the computational complexity associated to the prediction of the future state of a vertex. More precisely, we analyze two classes of local functions: the majority and the AND-OR rule (vertices take the And or the Or logic functions over the state of its ne...

In this paper we give upper bounds on the number of minimal separators and
potential maximal cliques of graphs w.r.t. two graph parameters, namely vertex
cover ($\operatorname{vc}$) and modular width ($\operatorname{mw}$). We prove
that for any graph, the number of minimal separators is
$\mathcal{O}^*(3^{\operatorname{vc}})$ and
$\mathcal{O}^*(1.61...