Resolving Conflicts for Lower-Bounded Clustering

This paper considers the effect of non-metric distances for lower-bounded clustering, i.e., the problem of computing a partition for a given set of objects with pairwise distance, such that each set has a certain minimum cardinality (as required for anonymisation or balanced facility location problems). We discuss lower-bounded clustering with the objective to minimise the maximum radius or diameter of the clusters. For these problems there exists a 2-approximation but only if the pairwise distance on the objects satisfies the triangle inequality, without this property no polynomial-time constant factor approximation is possible, unless P=NP. We try to resolve or at least soften this effect of non-metric distances by devising particular strategies to deal with violations of the triangle inequality (conflicts). With parameterised algorithmics, we find that if the number of such conflicts is not too large, constant factor approximations can still be computed efficiently. In particular, we introduce parameterised approximations with respect to not just the number of conflicts but also for the vertex cover number of the conflict graph (graph induced by conflicts). Interestingly, we salvage the approximation ratio of 2 for diameter while for radius it is only possible to show a ratio of 3. For the parameter vertex cover number of the conflict graph this worsening in ratio is shown to be unavoidable, unless FPT=W[2]. We further discuss improvements for diameter by choosing the (induced) P_3-cover number of the conflict graph as parameter and complement these by showing that, unless FPT=W[1], there exists no constant factor parameterised approximation with respect to the parameter split vertex deletion set

Shortest Distances as Enumeration Problem

We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements $(u, v, d(u, v))$ -- where $u$ and $v$ are vertices with shortest distance $d(u, v)$ -- are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs $(u, v, \infty)$, or excluding the self-distances $(u, u, 0)$) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.Comment: Updated version adds the study of space complexit

Fine-Grained Complexity of Regular Path Queries

A regular path query (RPQ) is a regular expression q that returns all node pairs (u, v) from a graph database that are connected by an arbitrary path labelled with a word from L(q). The obvious algorithmic approach to RPQ evaluation (called PG-approach), i. e., constructing the product graph between an NFA for q and the graph database, is appealing due to its simplicity and also leads to efficient algorithms. However, it is unclear whether the PG-approach is optimal. We address this question by thoroughly investigating which upper complexity bounds can be achieved by the PG-approach, and we complement these with conditional lower bounds (in the sense of the fine-grained complexity framework). A special focus is put on enumeration and delay bounds, as well as the data complexity perspective. A main insight is that we can achieve optimal (or near optimal) algorithms with the PG-approach, but the delay for enumeration is rather high (linear in the database). We explore three successful approaches towards enumeration with sub-linear delay: super-linear preprocessing, approximations of the solution sets, and restricted classes of RPQs

Alban Martin, L’Âge de Peer (Quand le choix du gratuit peut rapporter gros)

Internet, le Web 2.0, les blogs, le podcasting, les réseaux peer-to-peer — littéralement « pair à pair » qui permettent aux internautes (les « pairs ») de partager et d’échanger entre eux des films, de la musique ou tout autre ressource —, les procès des majors du divertissement contre le téléchargement illégal, la nouvelle loi pour le plan de développement de l’économie numérique : nous vivons depuis quelques années une véritable révolution culturelle. Et c’est bien tout un pan de l’économie..

Alban Martin, L’Âge de Peer (Quand le choix du gratuit peut rapporter gros)

Internet, le Web 2.0, les blogs, le podcasting, les réseaux peer-to-peer — littéralement « pair à pair » qui permettent aux internautes (les « pairs ») de partager et d’échanger entre eux des films, de la musique ou tout autre ressource —, les procès des majors du divertissement contre le téléchargement illégal, la nouvelle loi pour le plan de développement de l’économie numérique : nous vivons depuis quelques années une véritable révolution culturelle. Et c’est bien tout un pan de l’économie..

Guillaume Erner, Sociologie des tendances

« Les tendances, c’est tendance » (p.5). Ainsi commence le livre de Guillaume Erner qui propose une synthèse sur la sociologie des tendances. Même si la mode est née il y a déjà plusieurs siècles, le terme « tendance » est devenu un véritable argument marketing depuis ces dernières années. Et les sciences sociales sont face à une question difficile : pourquoi certains goûts et comportements sont-ils adoptés, de manière si soudaine et si éphémère, par une grande partie de la population ? C’est..