A Trichotomy for Regular Simple Path Queries on Graphs

Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regular simple path queries (RSPQs) find several applications in practice, yet they quickly become intractable, even for basic languages such as (aa)* or a*ba*. In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify the fragment that is maximal in the following sense: regular simple path queries can be evaluated in polynomial time for every regular language L that belongs to this fragment and evaluation is NP-complete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: Evaluations of RSPQs is either AC0, NL-complete or NP-complete in data complexity, depending on the regular language L. The fragment identified also admits a simple characterization in terms of regular expressions. Finally, we also discuss the complexity of the following decision problem: decide, given a language L, whether finding a regular simple path for L is tractable. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NL-complete for the first representation and PSPACE-complete for the other two. As a conclusion we extend our results from edge-labeled graphs to vertex-labeled graphs and vertex-edge labeled graphs.Comment: 15 pages, conference submissio

Approximable 1-Turn Routing Problems in All-Optical Mesh Networks

In all-optical networks, several communications can be transmitted through the same fiber link provided that they use different wavelengths. The MINIMUM ALL-OPTICAL ROUTING problem (given a list of pairs of nodes standing for as many point to point communication requests, assign to each request a route along with a wavelength so as to minimize the overall number of assigned wavelengths) has been paid a lot of attention and is known to be N P–hard. Rings, trees and meshes have thus been investigated as specific networks, but leading to just as many N P–hard problems. This paper investigates 1-turn routings in meshes (paths are allowed one turn only). We first show the MINIMUM LOAD 1-TURN ROUTING problem to be N P–hard but 2-APX (more generally, the MINIMUM LOAD k-CHOICES ROUTING problem is N P–hard but k-APX), then that the MINIMUM 1-TURN PATHS COLOURING problem is 4-APX (more generally, any d-segmentable routing of load L in a hypermesh of dimension d can be coloured with 2d(L−1)+1 colours at most). >From there, we prove the MINIMUM ALL-OPTICAL 1-TURN ROUTING problem to be APX

Eternal dominating sets on digraphs and orientations of graphs

We study the eternal dominating number and the m-eternal dominating number on digraphs. We generalize known results on graphs to digraphs. We also consider the problem "oriented (m-)eternal domination", consisting in finding an orientation of a graph that minimizes its eternal dominating number. We prove that computing the oriented eternal dominating number is NP-hard and characterize the graphs for which the oriented m-eternal dominating number is 2. We also study these two parameters on trees, cycles, complete graphs, complete bipartite graphs, trivially perfect graphs and different kinds of grids and products of graphs.Comment: 34 page

gMark: Schema-Driven Generation of Graphs and Queries

Massive graph data sets are pervasive in contemporary application domains. Hence, graph database systems are becoming increasingly important. In the experimental study of these systems, it is vital that the research community has shared solutions for the generation of database instances and query workloads having predictable and controllable properties. In this paper, we present the design and engineering principles of gMark, a domain- and query language-independent graph instance and query workload generator. A core contribution of gMark is its ability to target and control the diversity of properties of both the generated instances and the generated workloads coupled to these instances. Further novelties include support for regular path queries, a fundamental graph query paradigm, and schema-driven selectivity estimation of queries, a key feature in controlling workload chokepoints. We illustrate the flexibility and practical usability of gMark by showcasing the framework's capabilities in generating high quality graphs and workloads, and its ability to encode user-defined schemas across a variety of application domains.Comment: Accepted in November 2016. URL: http://ieeexplore.ieee.org/document/7762945/. in IEEE Transactions on Knowledge and Data Engineering 201

Incidence, a Scoring Positional Game on Graphs

Positional games have been introduced by Hales and Jewett in 1963 and have been extensively investigated in the literature since then. These games are played on a hypergraph where two players alternately select an unclaimed vertex of it. In the Maker-Breaker convention, if Maker manages to fully take a hyperedge, she wins, otherwise, Breaker is the winner. In the Maker-Maker convention, the first player to take a hyperedge wins. In both cases, the game stops as soon as Maker has taken a hyperedge. By definition, this family of games does not handle scores and cannot represent games in which players want to maximize a quantity. In this work, we introduce scoring positional games, that consist in playing on a hypergraph until all the vertices are claimed, and by defining the score as the number of hyperedges a player has fully taken. We focus here on Incidence, a scoring positional game played on a 2-uniform hypergraph, i.e. an undirected graph. In this game, two players alternately claim the vertices of a graph and score the number of edges for which they own both end vertices. In the Maker-Breaker version, Maker aims at maximizing the number of edges she owns, while Breaker aims at minimizing it. In the Maker-Maker version, both players try to take more edges than their opponent. We first give some general results on scoring positional games such that their membership in Milnor's universe and some general bounds on the score. We prove that, surprisingly, computing the score in the Maker-Breaker version of Incidence is PSPACE-complete whereas in the Maker-Maker convention, the relative score can be obtained in polynomial time. In addition, for the Maker-Breaker convention, we give a formula for the score on paths by using some equivalences due to Milnor's universe. This result implies that the score on cycles can also be computed in polynomial time

Genome-Wide Association Study Identifies First Locus Associated with Susceptibility to Cerebral Venous Thrombosis

Objective Cerebral venous thrombosis (CVT) is an uncommon form of stroke affecting mostly young individuals. Although genetic factors are thought to play a role in this cerebrovascular condition, its genetic etiology is not well understood. Methods A genome-wide association study was performed to identify genetic variants influencing susceptibility to CVT. A 2-stage genome-wide study was undertaken in 882 Europeans diagnosed with CVT and 1,205 ethnicity-matched control subjects divided into discovery and independent replication datasets. Results In the overall case-control cohort, we identified highly significant associations with 37 single nucleotide polymorphisms (SNPs) within the 9q34.2 region. The strongest association was with rs8176645 (combined p = 9.15 x 10(-24); odds ratio [OR] = 2.01, 95% confidence interval [CI] = 1.76-2.31). The discovery set findings were validated across an independent European cohort. Genetic risk score for this 9q34.2 region increases CVT risk by a pooled estimate OR = 2.65 (95% CI = 2.21-3.20, p = 2.00 x 10(-16)). SNPs within this region were in strong linkage disequilibrium (LD) with coding regions of the ABO gene. The ABO blood group was determined using allele combination of SNPs rs8176746 and rs8176645. Blood groups A, B, or AB, were at 2.85 times (95% CI = 2.32-3.52, p = 2.00 x 10(-16)) increased risk of CVT compared with individuals with blood group O. Interpretation We present the first chromosomal region to robustly associate with a genetic susceptibility to CVT. This region more than doubles the likelihood of CVT, a risk greater than any previously identified thrombophilia genetic risk marker. That the identified variant is in strong LD with the coding region of the ABO gene with differences in blood group prevalence provides important new insights into the pathophysiology of CVT. ANN NEUROL 2021Peer reviewe

Algorithmes et complexité des problèmes d'énumération pour l'évaluation de requêtes logiques

This thesis is dedicated to the evaluation of logical queries from the enumeration point of view. First, we deal with acyclic conjunctive formulas with inequalities; we show that such a query can be evaluated with linear delay in the size of the structure: this improves a result by Papadimitriou and Yannakakis. Then, we exhibit a subclass of acyclic formulas, so-called connex-acyclic formulas. Such queries can be evaluated with constant delay after some linear time preprocessing. We show that this result is maximal in the following sense: if the product of boolean matrices cannot be computed in linear time then any acyclic query is computable with constant delay after some linear time preprocessing if and only if it is connex-acyclic. Second, we prove that any MSO query over a class of bounded treewidth structures can be evaluated with a linear delay in the size of each solution after some linear preprocessing in the size of the structure. Third, we show that for each first-order query over bounded degree structures, one can compute the j-th solution of the query in constant time after some linear time preprocessing. Finally, we prove that unit interval graphs are of bounded local cliquewidth. Hence we deduce that any first-order statement over these graphs is decidable in linear time; Also, we show that this result is somehow maximal.Cette thèse est consacrée à l'évaluation de requêtes logiques du point de vue de l'énumération. Nous étudions quatre classes de requêtes. En premier lieu, nous nous intéressons aux formules conjonctives acycliques avec inégalités pour lesquelles nous améliorons un résultat de Papadimitriou et Yannakakis en montrant que de telles requêtes logiques peuvent être évaluées à délai linéaire en la taille de la structure. Nous exhibons ensuite la sous-classe des formules connexe-acycliques pour lesquelles l'évaluation de requêtes s'effectue à délai constant après prétraitement linéaire. Nous montrons que cette classe est maximale pour ce résultat dans le sens suivant: si le produit de matrices booléennes ne peut pas être calculé en temps linéaire alors toute requête conjonctive acyclique est évaluable à délai constant après prétra itement linéaire si et seulement si elle est connexe-acyclique. En second lieu, nous démontrons que toute requête MSO sur une classe de structures de largeur arborescente bornée peut être évaluée à délai linéaire en la taille de chaque solution produite après un prétraitement linéaire en la taille de la structure. En troisième lieu, nous montrons que, pour chaque requête en logique du premier ordre sur des structures de degré borné, il est possible de trouver en temps constant la j-ème solution dans un certain ordre après un prétraitement linéraire. Enfin, nous établissons que les graphes d'intervalles unitaires ont une largeur de clique localement bornée. D'où nous déduisons que tout énoncé du premier ordre sur ces graphes est décidable en temps linéaire; là encore, nous démontrons une certaine maximalité de ce résultat

MSO Queries on Tree Decomposable Structures are Computable with Constant Delay

International audienc

Algorithmes et complexité des problèmes d'énumération pour l'évaluation de requêtes logiques

Cette thèse est consacrée à l'évaluation de requêtes logiques du point de vue de l'énumération. Nous étudions quatre classes de requêtes. En premier lieu, nous nous intéressons aux formules conjonctives acycliques avec inégalités. Nous prouvons que de telles requêtes logiques peuvent être évaluées à délai linéaire en la taille de la structure. Nous exhibons ensuite la sous-classe des formules connexe-acycliques pour lesquelles l'évaluation de requêtes s'effectue à délai constant après prétraitement linéaire. Nous montrons que cette classe est maximale pour ce résultat dans le sens suivant: si le produit de deux matrices booléennes ne peut pas être calculé en temps linéaire, alors toute requête conjonctive acyclique est évaluable à délai constant après prétraitement linéaire si et seulement si elle est connexe-acyclique. En second lieu, nous démontrons que toute requête MSO sur une classe de structures de largeur arborescente bornée peut être évaluée à délai linéaire en la taille de chaque solution produite après un prétraitement linéaire en la taille de la structure. En troisième lieu, nous prouvons que, pour chaque requête en logique du premier ordre sur des structures de degré borné, il est possible de trouver en temps constant la j-ème solution dans un certain ordre après un prétraitement linéraire. Enfin, nous établissons que les graphes d'intervalles unitaires ont une largeur de clique localement bornée ; d'où nous déduisons que tout énoncé du premier ordre sur ces graphes est décidable en temps linéaire; là encore, nous démontrons une certaine maximalité de ce résultat.This thesis is dedicated to the evaluation of logical queries from the enumeration point of view. First, we deal with acyclic conjunctive formulas with inequalities; we show that such a query can be evaluated with linear delay in the size of the structure: this improves a result by Papadimitriou and Yannakakis. Then, we exhibit a subclass of acyclic formulas, so-called connex-acyclic formulas. Such queries can be evaluated with constant delay after some linear time preprocessing. We show that this result is maximal in the following sense: if the product of two boolean matrices cannot be computed in linear time then any acyclic conjunctive query is computable with constant delay after some linear time preprocessing if and only if it is connex-acyclic. Second, we prove that any MSO query over a class of bounded treewidth structures can be evaluated with a linear delay in the size of each solution after some linear preprocessing in the size of the structure. Third, we show that for each first-order query over bounded degree structures, one can compute the j-th solution of the query in constant time after some linear time preprocessing. Finally, we prove that unit interval graphs are of bounded local cliquewidth. Hence, we deduce that any first-order statement over these graphs is decidable in linear time; also, we show that this result is somehow maximal.CAEN-BU Sciences et STAPS (141182103) / SudocBORDEAUX1-Bib Rech. Maths-Info (335222209) / SudocSudocFranceF

Constant Delay Enumeration for Acyclic Conjunctive Queries over X-Doublebar Structures

We present an efficient answer enumeration algorithm for a fragment of Conditional XPath with variables, which is a first-order complete query language for unranked trees of bounded depth. Our algorithm requires linear precomputation time and constant delay for fixed queries, while depending linearly on the size of the query. It is based on a new enumeration algorithm for disjunctions of acyclic conjunctive queries on so called X-doublebar-structures that we introduce. Keywords: Logic, databases, enumeration, XML http://www.grappa.univ-lille3.fr/~niehren/Papers/X-doublebar/0.pd