Effective Edge-Fault-Tolerant Single-Source Spanners via Best (or Good) Swap Edges

Computing \emph{all best swap edges} (ABSE) of a spanning tree $T$ of a given $n$-vertex and $m$-edge undirected and weighted graph $G$ means to select, for each edge $e$ of $T$, a corresponding non-tree edge $f$, in such a way that the tree obtained by replacing $e$ with $f$ enjoys some optimality criterion (which is naturally defined according to some objective function originally addressed by $T$). Solving efficiently an ABSE problem is by now a classic algorithmic issue, since it conveys a very successful way of coping with a (transient) \emph{edge failure} in tree-based communication networks: just replace the failing edge with its respective swap edge, so as that the connectivity is promptly reestablished by minimizing the rerouting and set-up costs. In this paper, we solve the ABSE problem for the case in which $T$ is a \emph{single-source shortest-path tree} of $G$, and our two selected swap criteria aim to minimize either the \emph{maximum} or the \emph{average stretch} in the swap tree of all the paths emanating from the source. Having these criteria in mind, the obtained structures can then be reviewed as \emph{edge-fault-tolerant single-source spanners}. For them, we propose two efficient algorithms running in $O(m n +n^2 \log n)$ and $O(m n \log \alpha(m,n))$ time, respectively, and we show that the guaranteed (either maximum or average, respectively) stretch factor is equal to 3, and this is tight. Moreover, for the maximum stretch, we also propose an almost linear $O(m \log \alpha(m,n))$ time algorithm computing a set of \emph{good} swap edges, each of which will guarantee a relative approximation factor on the maximum stretch of $3/2$ (tight) as opposed to that provided by the corresponding BSE. Surprisingly, no previous results were known for these two very natural swap problems.Comment: 15 pages, 4 figures, SIROCCO 201

Weather types associated with flood, windstorm and synergic events in the Catalan coast

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2020, Tutor: Maria del Carmen LlasatThe aim of this work is to analyze the weather types following the Jenkinson and Collison methodology that have produced flood, windstorm and synergic events that have affected the Catalan coast during the period 1981-2015. To do this, the events to be analyzed were first selected from various databases and their distribution and temporal evolution were analyzed. In total, 186 flood events, 37 windstorms and 35 synergic events have been identified. The results point to the predominance of the cyclonic weather type in the three types of events and that the most damaging effects are those produced by synergic events

A Novel Algorithm for the All-Best-Swap-Edge Problem on Tree Spanners

Given a 2-edge connected, unweighted, and undirected graph $G$ with $n$ vertices and $m$ edges, a $\sigma$-tree spanner is a spanning tree $T$ of $G$ in which the ratio between the distance in $T$ of any pair of vertices and the corresponding distance in $G$ is upper bounded by $\sigma$. The minimum value of $\sigma$ for which $T$ is a $\sigma$-tree spanner of $G$ is also called the {\em stretch factor} of $T$. We address the fault-tolerant scenario in which each edge $e$ of a given tree spanner may temporarily fail and has to be replaced by a {\em best swap edge}, i.e. an edge that reconnects $T-e$ at a minimum stretch factor. More precisely, we design an $O(n^2)$ time and space algorithm that computes a best swap edge of every tree edge. Previously, an $O(n^2 \log^4 n)$ time and $O(n^2+m\log^2n)$ space algorithm was known for edge-weighted graphs [Bil\`o et al., ISAAC 2017]. Even if our improvements on both the time and space complexities are of a polylogarithmic factor, we stress the fact that the design of a $o(n^2)$ time and space algorithm would be considered a breakthrough.Comment: The paper has been accepted for publication at the 29th International Symposium on Algorithms and Computation (ISAAC 2018). 12 pages, 3 figure

Deterministic Digital Clustering of Wireless Ad Hoc Networks

We consider deterministic distributed communication in wireless ad hoc networks of identical weak devices under the SINR model without predefined infrastructure. Most algorithmic results in this model rely on various additional features or capabilities, e.g., randomization, access to geographic coordinates, power control, carrier sensing with various precision of measurements, and/or interference cancellation. We study a pure scenario, when no such properties are available. As a general tool, we develop a deterministic distributed clustering algorithm. Our solution relies on a new type of combinatorial structures (selectors), which might be of independent interest. Using the clustering, we develop a deterministic distributed local broadcast algorithm accomplishing this task in $O(\Delta \log^*N \log N)$ rounds, where $\Delta$ is the density of the network. To the best of our knowledge, this is the first solution in pure scenario which is only polylog$(n)$ away from the universal lower bound $\Omega(\Delta)$, valid also for scenarios with randomization and other features. Therefore, none of these features substantially helps in performing the local broadcast task. Using clustering, we also build a deterministic global broadcast algorithm that terminates within $O(D(\Delta + \log^* N) \log N)$ rounds, where $D$ is the diameter of the network. This result is complemented by a lower bound $\Omega(D \Delta^{1-1/\alpha})$, where $\alpha > 2$ is the path-loss parameter of the environment. This lower bound shows that randomization or knowledge of own location substantially help (by a factor polynomial in $\Delta$) in the global broadcast. Therefore, unlike in the case of local broadcast, some additional model features may help in global broadcast

Juana Doña y el manantial de la memoria. Memorias de las cárceles franquistas de mujeres (1978-2007)

Este artículo recoge y revisa las memorias de las presas políticas de la primera etapa del franquismo, publicadas desde 1978 hasta la actualidad, en el marco del llamado proceso de recuperación de la "memoria histórica" en España. El punto de partida es la publicación de Desde la noche y la niebla por la militante comunista Juana Doña (1918-2003), poniendo el acento en las peligrosas condiciones en que se dio la Transición española a la democracia. El texto analiza también, de manera sucinta, el cambio experimentado por estas condiciones a lo largo de los años noventa, con la emergencia, en el umbral del nuevo siglo, de un ambiente favorecedor simbolizado por la "Ley de Memoria Histórica" de 2007, bajo el último gobierno socialista.This article gathers and reviews the memoirs of political female prisoners during the first stage of Franco' regime, published since 1978 until now, within the framework of the so-called recovery of "historical memory" in Spain. The starting point is the publication of Desde la noche y la niebla, by communist militant Juana Doña (1918-2003) in 1978, placing the stress on the dangerous conditions of Spanish Transition to democracy. The text also analyzes, succinctly, the change of these conditions along the Nineties, with the emergence, on the threshold of the new Century, of a favourable environment symbolized by the "Historical Memory" Act of 2007, under the last Socialist government

Juana Doña y el manantial de la memoria. Memorias de las cárceles franquistas de mujeres (1978-2007)

This article gathers and reviews the memoirs of political female prisoners during the first stage of Franco’ regime, published since 1978 until now, within the framework of the so-called recovery of “historical memory” in Spain. The starting point is the publication of Desde la noche y la niebla, by communist militant Juana Doña (1918-2003) in 1978, placing the stress on the dangerous conditions of Spanish Transition to democracy. The text also analyzes, succinctly, the change of these conditions along the Nineties, with the emergence, on the threshold of the new Century, of a favourable environment symbolized by the “Historical Memory” Act of 2007, under the last Socialist government.Este artículo recoge y revisa las memorias de las presas políticas de la primera etapa del franquismo, publicadas desde 1978 hasta la actualidad, en el marco del llamado proceso de recuperación de la “memoria histórica” en España. El punto de partida es la publicación de Desde la noche y la niebla por la militante comunista Juana Doña (1918-2003), poniendo el acento en la peligrosas condiciones en que se dio la Transición española a la democracia. El texto analiza también, de manera sucinta, el cambio experimentado por estas condiciones a lo largo de los años noventa, con la emergencia, en el umbral del nuevo siglo, de un ambiente favorecedor simbolizado por la “Ley de Memoria Histórica” de 2007, bajo el último gobierno socialista