Bisection of Bounded Treewidth Graphs by Convolutions

In the Bisection problem, we are given as input an edge-weighted graph G. The task is to find a partition of V(G) into two parts A and B such that ||A| - |B|| <= 1 and the sum of the weights of the edges with one endpoint in A and the other in B is minimized. We show that the complexity of the Bisection problem on trees, and more generally on graphs of bounded treewidth, is intimately linked to the (min, +)-Convolution problem. Here the input consists of two sequences (a[i])^{n-1}_{i = 0} and (b[i])^{n-1}_{i = 0}, the task is to compute the sequence (c[i])^{n-1}_{i = 0}, where c[k] = min_{i=0,...,k}(a[i] + b[k - i]). In particular, we prove that if (min, +)-Convolution can be solved in O(tau(n)) time, then Bisection of graphs of treewidth t can be solved in time O(8^t t^{O(1)} log n * tau(n)), assuming a tree decomposition of width t is provided as input. Plugging in the naive O(n^2) time algorithm for (min, +)-Convolution yields a O(8^t t^{O(1)} n^2 log n) time algorithm for Bisection. This improves over the (dependence on n of the) O(2^t n^3) time algorithm of Jansen et al. [SICOMP 2005] at the cost of a worse dependence on t. "Conversely", we show that if Bisection can be solved in time O(beta(n)) on edge weighted trees, then (min, +)-Convolution can be solved in O(beta(n)) time as well. Thus, obtaining a sub-quadratic algorithm for Bisection on trees is extremely challenging, and could even be impossible. On the other hand, for unweighted graphs of treewidth t, by making use of a recent algorithm for Bounded Difference (min, +)-Convolution of Chan and Lewenstein [STOC 2015], we obtain a sub-quadratic algorithm for Bisection with running time O(8^t t^{O(1)} n^{1.864} log n)

Simultaneous Feedback Vertex Set: A Parameterized Perspective

Given a family of graphs $\mathcal{F}$, a graph $G$, and a positive integer $k$, the $\mathcal{F}$-Deletion problem asks whether we can delete at most $k$ vertices from $G$ to obtain a graph in $\mathcal{F}$. $\mathcal{F}$-Deletion generalizes many classical graph problems such as Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. A graph $G = (V, \cup_{i=1}^{\alpha} E_{i})$, where the edge set of $G$ is partitioned into $\alpha$ color classes, is called an $\alpha$-edge-colored graph. A natural extension of the $\mathcal{F}$-Deletion problem to edge-colored graphs is the $\alpha$-Simultaneous $\mathcal{F}$-Deletion problem. In the latter problem, we are given an $\alpha$-edge-colored graph $G$ and the goal is to find a set $S$ of at most $k$ vertices such that each graph $G_i \setminus S$, where $G_i = (V, E_i)$ and $1 \leq i \leq \alpha$, is in $\mathcal{F}$. In this work, we study $\alpha$-Simultaneous $\mathcal{F}$-Deletion for $\mathcal{F}$ being the family of forests. In other words, we focus on the $\alpha$-Simultaneous Feedback Vertex Set ($\alpha$-SimFVS) problem. Algorithmically, we show that, like its classical counterpart, $\alpha$-SimFVS parameterized by $k$ is fixed-parameter tractable (FPT) and admits a polynomial kernel, for any fixed constant $\alpha$. In particular, we give an algorithm running in $2^{O(\alpha k)}n^{O(1)}$ time and a kernel with $O(\alpha k^{3(\alpha + 1)})$ vertices. The running time of our algorithm implies that $\alpha$-SimFVS is FPT even when $\alpha \in o(\log n)$. We complement this positive result by showing that for $\alpha \in O(\log n)$, where $n$ is the number of vertices in the input graph, $\alpha$-SimFVS becomes W[1]-hard. Our positive results answer one of the open problems posed by Cai and Ye (MFCS 2014)

Student Involvement in Government: Antecedents and Outcomes

La implicació dels estudiants és un factor essencial perquè l’educació sigui efectiva. El govern estudiantil és una forma important d’implicació a través de la qual els estudiants representen els seus homòlegs, participen en els processos de presa de decisions de la universitat, i gestionen les activitats del campus. La implicació té un impacte visible en un mateix, en els companys, en el professorat, en els administradors universitaris i en l’entorn educatiu. Tanmateix, aquest concepte no ha estat objecte de l’atenció que mereix i són pocs els estudis sobre els seus antecedents i sobre els seus resultats. La importància d’aquesta recerca rau en la incorporació de teories (per exemple, intel·ligència emocional, aprenentatge experiencial) de diferents camps (el management, l’educació i la psicologia) per tractar aquest problema, és a dir, per comprendre millor els conceptes que contribueixen a la implicació i, viceversa, aquells que milloren amb la implicació. Així doncs, la qüestió principal és: Els estils d’aprenentatge, les competències (emocionals, socials i cognitives) i les filosofies operatives expliquen l’èxit posteducatiu dels estudiants que participen en experiències de govern estudiantil? En aquesta tesi es van realitzar tres estudis. El primer estudi analitza els estils d’aprenentatge, les competències (emocionals i socials) i les filosofies operatives com a antecedents de la implicació. El segon estudi analitza la relació entre les competències (emocionals, socials i cognitives) i la implicació. Finalment, el tercer estudi analitza l’impacte de la implicació sobre les variables de resultats relacionades amb l’èxit objectiu i subjectiu (ofertes de treball rebudes, satisfacció vital, satisfacció a la feina, etc.). Aquests estudis empren dissenys d'investigació no experimentals (investigació per enquestes). La unitat d'anàlisi és l'individu: estudiants internacionals d’MBA que van participar en un programa de desenvolupament de lideratge a ESADE Business School (Universitat Ramon Llull). Les dades es van recollir mitjançant enquestes (autoinforme i avaluació per parells) que consisteixen en mesures subjectives i objectives. La qualitat d’aquesta recerca s’avalua críticament, i es presenten possibles limitacions. A més, se n’especifiquen algunes conseqüències per a la recerca i per a la pràctica, així com suggeriments per a les institucions educatives, les empreses, els investigadors, els estudiants i els professionals. Finalment, es recomanen algunes línies de recerca futura.La implicación del estudiante es un factor esencial para que la educación sea efectiva. El gobierno estudiantil es una forma destacada de implicación a través de la cual los estudiantes representan a sus homólogos, participan en los procesos de toma de decisiones de la universidad, y gestionan las actividades del campus. La implicación tiene un impacto visible en uno mismo, en los compañeros, en el profesorado, en los administradores universitarios y en el entorno educativo. Pese a ello, este concepto no ha sido objeto de la atención que merece y son escasos los estudios sobre sus antecedentes y sobre sus resultados. La importancia de esta tesis radica en la incorporación de teorías (por ejemplo, inteligencia emocional, aprendizaje experiencial) de diversos campos (el management, la educación y la psicología) para abordar este tema, es decir, para entender mejor los conceptos que contribuyen a la implicación y, viceversa, aquellos que mejoran con la implicación. Así pues, la cuestión principal es: ¿Los estilos de aprendizaje, las competencias (emocionales, sociales y cognitivas) y las filosofías operativas explican el éxito posteducativo de los estudiantes que participan en experiencias de gobierno estudiantil? Para responder a la pregunta se realizaron tres estudios. El primer estudio analiza los estilos de aprendizaje, las competencias (emocionales y sociales) y las filosofías operativas como antecedentes de la implicación. El segundo estudio analiza la relación entre las competencias (emocionales, sociales y cognitivas) y la implicación. Finalmente, el tercer estudio analiza el impacto de la implicación sobre las variables relacionadas con el éxito objetivo y subjetivo (ofertas de trabajo recibidas, satisfacción vital, satisfacción en el trabajo, etc.). Estos estudios emplean diseños de investigación no experimentales (investigación por encuesta). La unidad de análisis es el individuo: estudiantes internacionales de MBA que participaron en un programa de desarrollo de liderazgo en ESADE Business School (Universitat Ramon Llull). Los datos se recolectaron mediante encuestas (autoinforme y evaluación por pares) que consisten en medidas subjetivas y objetivas. La calidad de esta investigación se evalúa críticamente y se presentan eventuales limitaciones. Además, se ofrecen posibles implicaciones en la investigación y en la práctica, así como sugerencias para las instituciones educativas, las empresas, los investigadores, los estudiantes y los profesionales. Finalmente, se recomiendan algunas líneas de investigación futura.Student involvement is crucial for the effectiveness and efficiency of education. Government is a major form of involvement through which students represent their peers, participate in the university’s decision-making processes, and manage on-campus activities of organizations and clubs. Involvement has a visible impact on oneself, peers, faculty, administrators, and environment (educational experience). Yet, this concept has not received the proper attention, and research on its antecedents and outcomes remains scarce. The significance of this thesis lies in the incorporation of theories (e.g. emotional intelligence, experiential learning) from various fields (management, education, and psychology) to address this issue i.e. to better understand the concepts that contribute to involvement and, conversely, those that involvement contributes to. Hence, the main question is: Do learning styles, competencies (emotional, social, and cognitive), and operating philosophies account for post-education success of students involved in government experiences? This thesis comprises three studies. The first study analyzes learning styles, emotional and social competencies, and operating philosophies as antecedents of involvement. The second study analyzes the relationship between emotional, social, and cognitive competencies and involvement. Finally, the third study analyzes the impact of involvement on variables related to objective and subjective success (job offers received, life satisfaction, job satisfaction, etc.). These studies employ non-experimental research designs (survey research). The unit of analysis is the individual: international MBA students that participated in a leadership-development program at ESADE Business School (Universitat Ramon Llull). Data were collected using surveys (self-report and peer assessment) that consist of subjective and objective measures. The quality of this research is critically assessed and possible limitations and threats to validity are presented. Furthermore, implications for research and practice are provided in addition to suggestions that can be useful to educational institutions, organizations, researchers, students, and practitioners. Finally, future research lines are recommended

Towards Object-Centric Scene Understanding

Visual perception for autonomous agents continues to attract community attention due to the disruptive technologies and the wide applicability of such solutions. Autonomous Driving (AD), a major application in this domain, promises to revolutionize our approach to mobility while bringing critical advantages in limiting accident fatalities. Fueled by recent advances in Deep Learning (DL), more computer vision tasks are being addressed using a learning paradigm. Deep Neural Networks (DNNs) succeeded consistently in pushing performances to unprecedented levels and demonstrating the ability of such approaches to generalize to an increasing number of difficult problems, such as 3D vision tasks. In this thesis, we address two main challenges arising from the current approaches. Namely, the computational complexity of multi-task pipelines, and the increasing need for manual annotations. On the one hand, AD systems need to perceive the surrounding environment on different levels of detail and, subsequently, take timely actions. This multitasking further limits the time available for each perception task. On the other hand, the need for universal generalization of such systems to massively diverse situations requires the use of large-scale datasets covering long-tailed cases. Such requirement renders the use of traditional supervised approaches, despite the data readily available in the AD domain, unsustainable in terms of annotation costs, especially for 3D tasks. Driven by the AD environment nature and the complexity dominated (unlike indoor scenes) by the presence of other scene elements (mainly cars and pedestrians) we focus on the above-mentioned challenges in object-centric tasks. We, then, situate our contributions appropriately in fast-paced literature, while supporting our claims with extensive experimental analysis leveraging up-to-date state-of-the-art results and community-adopted benchmarks

The complexity of dominating set reconfiguration

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by $O(n)$, where $n$ is the number of vertices in the input graph