arXiv subjects

Anthony Perez

Publications and source records attributed to Anthony Perez.

At least 19 recordsLinked to original sources

arXiv2026

On the parameterized complexity of Broadcast Independence and Broadcast Packing

A broadcast on a connected graph is a function f that assigns each vertex v an integer f(v) with 0 <= f(v) <= ecc(v) where ecc(v) denotes the eccentricity of v. A vertex u hears a broadcasting vertex v (with f(v)>0) if u is at distance at most f(v) from v. Beyond the classical broadcast domination problem, where every vertex is required to hear at least one vertex, two variants raise intriguing combinatorial and algorithmic questions. In an independent broadcast, no broadcasting vertex hears another broadcasting vertex, while a broadcast packing requires that every vertex hears at most one broadcasting vertex. The corresponding problems Broadcast Independence and Broadcast Packing ask for broadcasts of values at least k under these constraints, where the value is the sum of the broadcast values. We initiate a systematic study of the parameterized complexity of such problems. We prove that Broadcast Independence and Broadcast Packing are FPT parameterized by the treewidth plus the diameter of G, with a family of dynamic-programming algorithms over nice tree decompositions. We obtain as a corollary that both problems are FPT parameterized by k and the treewidth of G and XP for treewidth only. The latter result shows that the known algorithm for trees (Bessy and Rautenbach, DAM 2022) can indeed be extended to bounded treewidth graphs. On the negative side, we show that Broadcast Independence is W[1]-hard parameterized by the pathwidth of G. Note that this result completes the picture for parameter k and treewidth for Broadcast Independence since it is known to be W[1]-hard for k only. We complement these results by showing that a weighted version of both problems, where the input comes with a weight function on the edges, is W[1]-hard parameterized by the vertex cover of G. Finally, we provide a constant-factor approximation algorithm parameterized by treewidth for Broadcast Independence.

cs.DS↗

arXiv2024

Induced Minor Models. II. Sufficient conditions for polynomial-time detection of induced minors

The $H$-Induced Minor Containment problem ($H$-IMC) consists in deciding if a fixed graph $H$ is an induced minor of a graph $G$ given as input, that is, whether $H$ can be obtained from $G$ by deleting vertices and contracting edges. Equivalently, the problem asks if there exists an induced minor model of $H$ in $G$, that is, a collection of disjoint subsets of vertices of $G$, each inducing a connected subgraph, such that contracting each subgraph into a single vertex results in $H$. It is known that $H$-IMC is NP-complete for several graphs $H$, even when $H$ is a tree. In this work, we investigate which properties of $H$ guarantee the existence of an induced minor model whose structure can be leveraged to solve the problem in polynomial time. This allows us to identify four infinite families of graphs $H$ that enjoy such properties. Moreover, we show that if the input graph $G$ excludes long induced paths, then $H$-IMC is polynomial-time solvable for any fixed graph $H$. As a byproduct of our results, this implies that $H$-IMC is polynomial-time solvable for all graphs $H$ with at most $5$ vertices, except for three open cases.

cs.DS↗

arXiv2024

Hypersparse Traffic Matrices from Suricata Network Flows using GraphBLAS

Hypersparse traffic matrices constructed from network packet source and destination addresses is a powerful tool for gaining insights into network traffic. SuiteSparse: GraphBLAS, an open source package or building, manipulating, and analyzing large hypersparse matrices, is one approach to constructing these traffic matrices. Suricata is a widely used open source network intrusion detection software package. This work demonstrates how Suricata network flow records can be used to efficiently construct hypersparse matrices using GraphBLAS.

cs.DC↗

arXiv2024

Induced Minor Models. I. Structural Properties and Algorithmic Consequences

A graph $H$ is said to be an induced minor of a graph $G$ if $H$ can be obtained from $G$ by a sequence of vertex deletions and edge contractions. Equivalently, $H$ is an induced minor of $G$ if there exists an induced minor model of $H$ in $G$, that is, a collection of pairwise disjoint subsets of vertices of $G$ labeled by the vertices of $H$, each inducing a connected subgraph in $G$, such that two vertices of $H$ are adjacent if and only if there is an edge in $G$ between the corresponding subsets. In this paper, we investigate structural properties of induced minor models, including bounds on treewidth and chromatic number of the subgraphs induced by minimal induced minor models. It is known that for some graphs $H$, testing whether a given graph $G$ contains $H$ as an induced minor is an NP-complete problem. Nevertheless, as algorithmic applications of our structural results, we make use of recent developments regarding tree-independence number to show that if $H$ is the $4$-wheel, the $5$-vertex complete graph minus an edge, or a complete bipartite graph $K_{2,q}$, then there is a polynomial-time algorithm to find in a given graph $G$ an induced minor model of $H$ in $G$, if there is one. We also develop an alternative polynomial-time algorithm for recognizing graphs that do not contain $K_{2,3}$ as an induced minor, which revolves around the idea of detecting the induced subgraphs whose presence is forced when the input graph contains $K_{2,3}$ as an induced minor, using the so-called shortest path detector. It turns out that all these induced subgraphs are Truemper configurations.

math.CO↗

arXiv2023

An improved kernelization algorithm for Trivially Perfect Editing

In the Trivially Perfect Editing problem one is given an undirected graph $G = (V,E)$ and an integer $k$ and seeks to add or delete at most $k$ edges in $G$ to obtain a trivially perfect graph. In a recent work, Dumas, Perez and Todinca [Algorithmica 2023] proved that this problem admits a kernel with $O(k^3)$ vertices. This result heavily relies on the fact that the size of trivially perfect modules can be bounded by $O(k^2)$ as shown by Drange and Pilipczuk [Algorithmica 2018]. To obtain their cubic vertex-kernel, Dumas, Perez and Todinca [Algorithmica 2023] then showed that a more intricate structure, so-called \emph{comb}, can be reduced to $O(k^2)$ vertices. In this work we show that the bound can be improved to $O(k)$ for both aforementioned structures and thus obtain a kernel with $O(k^2)$ vertices. Our approach relies on the straightforward yet powerful observation that any large enough structure contains unaffected vertices whose neighborhood remains unchanged by an editing of size $k$, implying strong structural properties.

cs.DS↗

arXiv2023

Superpixels algorithms through network community detection

Community detection is a powerful tool from complex networks analysis that finds applications in various research areas. Several image segmentation methods rely for instance on community detection algorithms as a black box in order to compute undersegmentations, i.e. a small number of regions that represent areas of interest of the image. However, to the best of our knowledge, the efficiency of such an approach w.r.t. superpixels, that aim at representing the image at a smaller level while preserving as much as possible original information, has been neglected so far. The only related work seems to be the one by Liu et. al. (IET Image Processing, 2022) that developed a superpixels algorithm using a so-called modularity maximization approach, leading to relevant results. We follow this line of research by studying the efficiency of superpixels computed by state-of-the-art community detection algorithms on a 4-connected pixel graph, so-called pixel-grid. We first detect communities on such a graph and then apply a simple merging procedure that allows to obtain the desired number of superpixels. As we shall see, such methods result in the computation of relevant superpixels as emphasized by both qualitative and quantitative experiments, according to different widely-used metrics based on ground-truth comparison or on superpixels only. We observe that the choice of the community detection algorithm has a great impact on the number of communities and hence on the merging procedure. Similarly, small variations on the pixel-grid may provide different results from both qualitative and quantitative viewpoints. For the sake of completeness, we compare our results with those of several state-of-the-art superpixels algorithms as computed by Stutz et al. (Computer Vision and Image Understanding, 2018).

cs.CV↗

arXiv2022

On graphs coverable by k shortest paths

We show that if the edges or vertices of an undirected graph $G$ can be covered by $k$ shortest paths, then the pathwidth of $G$ is upper-bounded by a single-exponential function of $k$. As a corollary, we prove that the problem Isometric Path Cover with Terminals (which, given a graph $G$ and a set of $k$ pairs of vertices called terminals, asks whether $G$ can be covered by $k$ shortest paths, each joining a pair of terminals) is FPT with respect to the number of terminals. The same holds for the similar problem Strong Geodetic Set with Terminals (which, given a graph $G$ and a set of $k$ terminals, asks whether there exist $\binom{k}{2}$ shortest paths covering $G$, each joining a distinct pair of terminals). Moreover, this implies that the related problems Isometric Path Cover and Strong Geodetic Set (defined similarly but where the set of terminals is not part of the input) are in XP with respect to parameter $k$.

cs.DM↗

arXiv2022

Polynomial kernels for edge modification problems towards block and strictly chordal graphs

We consider edge modification problems towards block and strictly chordal graphs, where one is given an undirected graph $G = (V,E)$ and an integer $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a block graph or a strictly chordal graph. The completion and deletion variants of these problems are defined similarly by only allowing edge additions for the former and only edge deletions for the latter. Block graphs are a well-studied class of graphs and admit several characterizations, e.g. they are diamond-free chordal graphs. Strictly chordal graphs, also referred to as block duplicate graphs, are a natural generalization of block graphs where one can add true twins of cut-vertices. Strictly chordal graphs are exactly dart and gem-free chordal graphs. We prove the NP-completeness for most variants of these problems and provide $O(k^2)$ vertex-kernels for Block Graph Editing and Block Graph Deletion, $O(k^3)$ vertex-kernels for Strictly Chordal Completion and Strictly Chordal Deletion and a $O(k^4)$ vertex-kernel for Strictly Chordal Editing.

cs.DS↗

arXiv2021

A cubic vertex-kernel for Trivially Perfect Editing

We consider the Trivially Perfect Editing problem, where one is given an undirected graph $G = (V,E)$ and a parameter $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a trivially perfect graph. The related Trivially Perfect Completion and Trivially Perfect Deletion problems are obtained by only allowing edge additions or edge deletions, respectively. Trivially perfect graphs are both chordal and cographs, and have applications related to the tree-depth width parameter and to social network analysis. All variants of the problem are known to be NP-Complete and to admit so-called polynomial kernels. More precisely, the existence of an $O(k^3)$ vertex-kernel for Trivially Perfect Completion was announced by Guo (ISAAC 2007) but without a stand-alone proof. More recently, Drange and Pilipczuk (Algorithmica 2018) provided $O(k^7)$ vertex-kernels for these problems and left open the existence of cubic vertex-kernels. In this work, we answer positively to this question for all three variants of the problem.

cs.DS↗

arXiv2020

On the complexity of Broadcast Domination and Multipacking in digraphs

We study the complexity of the two dual covering and packing distance-based problems Broadcast Domination and Multipacking in digraphs. A dominating broadcast of a digraph $D$ is a function $f:V(D)\to\mathbb{N}$ such that for each vertex $v$ of $D$, there exists a vertex $t$ with $f(t)>0$ having a directed path to $v$ of length at most $f(t)$. The cost of $f$ is the sum of $f(v)$ over all vertices $v$. A multipacking is a set $S$ of vertices of $D$ such that for each vertex $v$ of $D$ and for every integer $d$, there are at most $d$ vertices from $S$ within directed distance at most $d$ from $v$. The maximum size of a multipacking of $D$ is a lower bound to the minimum cost of a dominating broadcast of $D$. Let Broadcast Domination denote the problem of deciding whether a given digraph $D$ has a dominating broadcast of cost at most $k$, and Multipacking the problem of deciding whether $D$ has a multipacking of size at least $k$. It is known that Broadcast Domination is polynomial-time solvable for the class of all undirected graphs (that is, symmetric digraphs), while polynomial-time algorithms for Multipacking are known only for a few classes of undirected graphs. We prove that Broadcast Domination and Multipacking are both NP-complete for digraphs, even for planar layered acyclic digraphs of small maximum degree. Moreover, when parameterized by the solution cost/solution size, we show that the problems are W-hard. We also show that Broadcast Domination is FPT on acyclic digraphs, and that it does not admit a polynomial kernel for such inputs, unless the polynomial hierarchy collapses to its third level. In addition, we show that both problems are FPT when parameterized by the solution cost/solution size together with the maximum out-degree, and as well, by the vertex cover number. Finally, we give for both problems polynomial-time algorithms for some subclasses of acyclic digraphs.

cs.DS↗

arXiv2019

Semi-Supervised Multitask Learning on Multispectral Satellite Images Using Wasserstein Generative Adversarial Networks (GANs) for Predicting Poverty

Obtaining reliable data describing local poverty metrics at a granularity that is informative to policy-makers requires expensive and logistically difficult surveys, particularly in the developing world. Not surprisingly, the poverty stricken regions are also the ones which have a high probability of being a war zone, have poor infrastructure and sometimes have governments that do not cooperate with internationally funded development efforts. We train a CNN on free and publicly available daytime satellite images of the African continent from Landsat 7 to build a model for predicting local economic livelihoods. Only 5% of the satellite images can be associated with labels (which are obtained from DHS Surveys) and thus a semi-supervised approach using a GAN (similar to the approach of Salimans, et al. (2016)), albeit with a more stable-to-train flavor of GANs called the Wasserstein GAN regularized with gradient penalty(Gulrajani, et al. (2017)) is used. The method of multitask learning is employed to regularize the network and also create an end-to-end model for the prediction of multiple poverty metrics.

cs.CV↗

arXiv2017

Poverty Prediction with Public Landsat 7 Satellite Imagery and Machine Learning

Obtaining detailed and reliable data about local economic livelihoods in developing countries is expensive, and data are consequently scarce. Previous work has shown that it is possible to measure local-level economic livelihoods using high-resolution satellite imagery. However, such imagery is relatively expensive to acquire, often not updated frequently, and is mainly available for recent years. We train CNN models on free and publicly available multispectral daytime satellite images of the African continent from the Landsat 7 satellite, which has collected imagery with global coverage for almost two decades. We show that despite these images' lower resolution, we can achieve accuracies that exceed previous benchmarks.

stat.ML↗

arXiv2015

A community role approach to assess social capitalists visibility in the Twitter network

In the context of Twitter, social capitalists are specific users trying to increase their number of followers and interactions by any means. These users are not healthy for the service, because they are either spammers or real users flawing the notions of influence and visibility. Studying their behavior and understanding their position in Twit-ter is thus of important interest. It is also necessary to analyze how these methods effectively affect user visibility. Based on a recently proposed method allowing to identify social capitalists, we tackle both points by studying how they are organized, and how their links spread across the Twitter follower-followee network. To that aim, we consider their position in the network w.r.t. its community structure. We use the concept of community role of a node, which describes its position in a network depending on its connectiv-ity at the community level. However, the topological measures originally defined to characterize these roles consider only certain aspects of the community-related connectivity, and rely on a set of empirically fixed thresholds. We first show the limitations of these measures, before extending and generalizing them. Moreover, we use an unsupervised approach to identify the roles, in order to provide more flexibility relatively to the studied system. We then apply our method to the case of social capitalists and show they are highly visible on Twitter, due to the specific roles they hold.

cs.SI↗

arXiv2014

Identifying the Community Roles of Social Capitalists in the Twitter Network

In the context of Twitter, social capitalists are specific users trying to increase their number of followers and interactions by any means. These users are not healthy for the Twitter network since they flaw notions of influence and visibility. Indeed, it has recently been observed that they are real and active users that can help malicious users such as spammers gaining influence. Studying their behavior and understanding their position in Twitter is thus of important interest. A recent work provided an efficient way to detect social capitalists using two simple topological measures. Based on this detection method, we study how social capitalists are distributed over Twitter's friend-to-follower network. We are especially interested in analyzing how they are organized, and how their links spread across the network. Answering these questions allows to know whether the social capitalism methods increase the actual visibility on the service. To that aim, we study the position of social capitalists on Twitter w.r.t. the community structure of the network. We base our work on the concept of community role of a node, which describes its position in a network depending on its connectivity at the community level. The topological measures originally defined to characterize these roles consider only some aspects of community-related connectivity and rely on a set of empirically fixed thresholds. We first show the limitations of such measures and then extend and generalize them by considering new aspects of the community-related connectivity. Moreover, we use an unsupervised approach to distinguish the roles, in order to provide more flexibility relatively to the studied system. We then apply our method to the case of social capitalists and show that they are highly visible on Twitter, due to the specific roles they occupy.

cs.SI↗

arXiv2014

Conflict Packing: an unifying technique to obtain polynomial kernels for editing problems on dense instances

We develop a technique that we call Conflict Packing in the context of kernelization, obtaining (and improving) several polynomial kernels for editing problems on dense instances. We apply this technique on several well-studied problems: Feedback Arc Set in (Bipartite) Tournaments, Dense Rooted Triplet Inconsistency and Betweenness in Tournaments. For the former, one is given a (bipartite) tournament $T = (V,A)$ and seeks a set of at most $k$ arcs whose reversal in $T$ results in an acyclic (bipartite) tournament. While a linear vertex-kernel is already known for the first problem, using the Conflict Packing allows us to find a so-called safe partition, the central tool of the kernelization algorithm in, with simpler arguments. For the case of bipartite tournaments, the same technique allows us to obtain a quadratic vertex-kernel. Again, such a kernel was already known to exist, using the concept of so-called bimodules. We believe however that providing an unifying technique to cope with such problems is interesting. Regarding Dense Rooted Triplet Inconsistency, one is given a set of vertices $V$ and a dense collection $\mathcal{R}$ of rooted binary trees over three vertices of $V$ and seeks a rooted tree over $V$ containing all but at most $k$ triplets from $\mathcal{R}$. As a main consequence of our technique, we prove that the Dense Rooted Triplet Inconsistency problem admits a linear vertex-kernel. This result improves the best known bound of $O(k^2)$ vertices for this problem. Finally, we use this technique to obtain a linear vertex-kernel for Betweenness in Tournaments, where one is given a set of vertices $V$ and a dense collection $\mathcal{R}$ of so-called betweenness triplets and seeks a linear ordering of the vertices containing all but at most $k$ triplets from $\mathcal{R}$.

cs.DS↗

arXiv2013

Identification de rôles communautaires dans des réseaux orientés appliquée à Twitter

The notion of community structure is particularly useful when analyzing complex networks, because it provides an intermediate level, compared to the more classic global (whole network) and local (node neighborhood) approaches. The concept of community role of a node was derived from this base, in order to describe the position of a node in a network depending on its connectivity at the community level. However, the existing approaches are restricted to undirected networks, use topological measures which do not consider all aspects of community-related connectivity, and their role identification methods are not generalizable to all networks. We tackle these limitations by generalizing and extending the measures, and using an unsupervised approach to determine the roles. We then illustrate the applicability of our method by analyzing a Twitter network.We show how our modifications allow discovering the fact some particular users called social capitalists occupy very specific roles in this system. --- La notion de structure de communautés est particulièrement utile pour étudier les réseaux complexes, car elle amène un niveau d'analyse intermédiaire, par opposition aux plus classiques niveaux local (voisinage des noeuds) et global (réseau entier). Le concept de rôle communautaire permet de décrire le positionnement d'un noeud en fonction de sa connectivité communautaire. Cependant, les approches existantes sont restreintes aux réseaux non-orientés, utilisent des mesures topologiques ne considérant pas tous les aspects de la connectivité communautaire, et des méthodes d'identification des rôles non-généralisables à tous les réseaux. Nous proposons de résoudre ces problèmes en généralisant les mesures existantes, et en utilisant une méthode non-supervisée pour déterminer les rôles. Nous illustrons l'intérêt de notre méthode en l'appliquant au réseau de Twitter. Nous montrons que nos modifications mettent en évidence les rôles spécifiques d'utilisateurs particuliers du réseau, nommés capitalistes sociaux.

cs.SI↗

arXiv2013

Rôle communautaire des capitalistes sociaux dans Twitter

Les capitalistes sociaux sont des utilisateurs de médias sociaux tels que Twitter, appliquant diverses techniques pour obtenir un maximum de visibilité. Ils peuvent être néfastes à l'équilibre du service, dans la mesure où leurs comptes, en gagnant en importance sans réelle raison de contenu, rendent difficile l'accès à un contenu pertinent. Dans ce travail, nous nous intéressons à leur caractérisation d'un point de vue purement topologique, i.e. sans considérer la nature des contenus partagés. Nous utilisons pour cela la notion de rôle communautaire, qui est basée sur la structure de communautés du réseau étudié. Nous apportons des modifications à des mesures précédemment définies à cet effet, et proposons une méthode objective de détection des rôles. Nous appliquons ensuite notre méthode à l'analyse d'un réseau représentant Twitter. Nos résultats montrent que les rôles que nous identifions via nos mesures se révèlent particulièrement cohérents par rapport aux capitalistes sociaux du réseau Twitter, dont le comportement est clairement identifié---Social capitalists are social media users taking advantage of various methods to maximize their visibility. This results in artificially important accounts, in the sense this importance is not backed by any real content. The risk is then to see those accounts hiding relevant contents and therefore preventing other users to access them. In this work, we want to characterize social capitalists from a purely topological perspective, i.e. without considering the nature of the shared contents. For this purpose, we use the notion of community role, based on the community structure of the studied network. We modify some measures previously designed for this matter, and propose an objective method to determine roles. We then apply this method to the analysis of a Twitter network. Our results show the roles identified through our measures are particularly consistent with Twitter's social capitalists, whose behavior was clearly identified.

cs.CY↗

arXiv2012

Linear vertex-kernels for several dense ranking r-CSPs

A Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r >= 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The objective is to decide if there exists a ranking of the vertices satisfying all but at most k constraints. Famous ranking r-CSP include the Feedback Arc Set in Tournaments and Betweenness in Tournaments problems. We consider these problems from the kernelization viewpoint. We prove that so-called l_r-simply characterized ranking r-CSPs admit linear vertex-kernels whenever they admit constant-factor approximation algorithms. This implies that r-Betweenness in Tournaments and r-Transitive Feedback Arc Set In Tournaments, two natural generalizations of the previously mentioned problems, admit linear vertex-kernels. Moreover, we introduce another generalization of Feedback Arc Set in Tournaments, which does not fit the aforementioned framework. We obtain a 5-approximation and a linear vertex-kernel for this problem.

cs.DM↗