Every day it is more common to hear around us about the publication of studies, surveys or statistical results about the well-being of people, workers, women in a given country. Indeed, as university professors, our work cannot be independent of the level of well-being of our students. So, in this work, we propose a methodology to asses the students well-being inside a course implementation by what we call the educational well-being index (EWI). We start with a survey that gathers those factors that computing courses’ students at our university –of two different levels and majors– consider most important. Our second step is the evaluation –by a group of teachers– of the presence of those factors in different educational models of implementation of the courses. We use principal component analysis to extract, from the student data, the valuations that they expressed in the survey: the principal component of their own measurements on well-being. We work only with the coefficients of the first dimension of the principal component. The third step is a (subjective) valuation of the topics addressed in the survey when considering a particular educational model. Finally, we gather everything together to obtain a well-being index of an educational model that allows their comparison. Besides the methodology, we present and analyze the values obtained from our case study.

We introduce the multicolored graph realization problem (MGR). The input to this problem is a colored graph (G,φ), i.e., a graph G together with a coloring φ on its vertices. We associate each colored graph (G,φ) with a cluster graph (Gφ) in which, after collapsing all vertices with the same color to a node, we remove multiple edges and self-loops. A set of vertices S is multicolored when S has exactly one vertex from each color class. The MGR problem is to decide whether there is a multicolored set S so that, after identifying each vertex in S with its color class, G[S] coincides with Gφ. The MGR problem is related to the well-known class of generalized network problems, most of which are NP-hard, like the generalized Minimum Spanning Tree problem. The MGR is a generalization of the multicolored clique problem, which is known to be W[1]-hard when parameterized by the number of colors. Thus, MGR remains W[1]-hard, when parameterized by the size of the cluster graph. These results imply that the MGR problem is W[1]-hard when parameterized by any graph parameter on Gφ, among which lies treewidth. Consequently, we look at the instances of the problem in which both the number of color classes and the treewidth of Gφ are unbounded. We consider three natural such graph classes: chordal graphs, convex bipartite graphs and 2-dimensional grid graphs. We show that MGR is NP-complete when Gφ is either chordal, biconvex bipartite, complete bipartite or a 2-dimensional grid. Our reductions show that the problem remains hard even when the maximum number of vertices in a color class is 3. In the case of the grid, the hardness holds even for graphs with bounded degree. We provide a complexity dichotomy with respect to cluster size.

Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that has a neighbor in the other set. In this work we are interested in providing asymptotically almost surely upper bounds on the minimum vertex bisection of random d-regular graphs, for constant values of d. Our approach is based on analyzing a greedy algorithm by using the Differential Equations Method. In this way, we obtain the first known non trivial upper bounds for the vertex bisection number in random regular graphs. The numerical approximations of these theoretical bounds are compared with the emprical ones, and with the lower bounds from Kolesnik and Wormald: “Lower Bounds for the Isoperimetric Numbers of Random Regular Graphs”, SIAM J. on Disc. Math. 28(1), 553-575, 2014.

We propose the FwLTR and BwLTR, two new centrality measures based on the Linear Threshold model. In contrast to the Linear Threshold rank (LTR), these measures differentiate between the incoming and the outgoing neighborhoods of the activation set that initiates the spreading process. Their rankings are distinguishable from the rest of the centrality measures considered traditionally. However, LTR and BwLTR behave quite similarly, while FwLTR is clearly different.

We study the concept of compactor, which may be seen as a counting-analogue of kernelization in counting parameterized complexity. For a function F:Sigma^* -> N and a parameterization kappa: Sigma^* -> N, a compactor (P,M) consists of a polynomial-time computable function P, called condenser, and a computable function M, called extractor, such that F=M o P, and the condensing P(x) of x has length at most s(kappa(x)), for any input x in Sigma^*. If s is a polynomial function, then the compactor is said to be of polynomial-size. Although the study on counting-analogue of kernelization is not unprecedented, it has received little attention so far. We study a family of vertex-certified counting problems on graphs that are MSOL-expressible; that is, for an MSOL-formula phi with one free set variable to be interpreted as a vertex subset, we want to count all A subseteq V(G) where |A|=k and (G,A) models phi. In this paper, we prove that every vertex-certified counting problems on graphs that is MSOL-expressible and treewidth modulable, when parameterized by k, admits a polynomial-size compactor on H-topological-minor-free graphs with condensing time O(k^2n^2) and decoding time 2^{O(k)}. This implies the existence of an FPT-algorithm of running time O(n^2 k^2)+2^{O(k)}. All aforementioned complexities are under the Uniform Cost Measure (UCM) model where numbers can be stored in constant space and arithmetic operations can be done in constant time.

The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is polynomial on an n-vertex undirected graph, which allows the behaviour of the process on undirected graphs to be analysed using the Markov chain Monte Carlo method. We show that this does not extend to directed graphs by exhibiting an infinite family of directed graphs for which the expected absorption time is exponential in the number of vertices. However, for regular directed graphs, we give the expected absorption time is blog n lower bound and an explicit quadratic upper bound. We exhibit families of graphs matching these bounds and give improved bounds for other families of graphs, based on isoperimetric number. Our results are obtained via stochastic dominations which we demonstrate by establishing a coupling in a related continuous-time model. The coupling also implies several natural domination results regarding the fixation probability of the original (discrete-time) process, resolving a conjecture of Shakarian, Roos and Johnson.

What is the role that a university should play in the spreading of cutting-edge technologies? It is argued here that one possibility is to bring focused cutting-edge technology courses in the standard curriculum. It is contended that such courses have shorter life-spans than conventional subjects and, consequently, their implementation needs to be more dynamic. These claims are backed by discussing the life-cycle of an Android course running biannually from Spring 2010 to Spring 2013 at Universitat Politecnica de Catalunya. The rise phase of this course (which lasted two semesters) was a challenging experience that motivated students and lecturers to play a cooperative and active role in the creation of true working Android applications. The course held stable for two semesters while student motivation began to fall as smart phones increasingly became everyday objects. During these two phases the course was offered as extra curricular in the undergraduate phase. Two added factors were instrumental in the decline (or fall) phase: the availability of on-line information and the fact that the course became a requirement of a master’s curriculum.

An orchestration is a multi-threaded computation that invokes a number of remote services. In practice, the responsiveness of a web-service fluctuates with demand; during surges in activity service responsiveness may be degraded, perhaps even to the point of failure. An uncertainty profile formalizes a user's perception of the effects of stress on an orchestration of web-services; it describes a strategic situation, modelled by a zero-sum angel–daemon game. Stressed web-service scenarios are analysed, using game theory, in a realistic way, lying between over-optimism (services are entirely reliable) and over-pessimism (all services are broken). The ‘resilience’ of an uncertainty profile can be assessed using the valuation of its associated zero-sum game. In order to demonstrate the validity of the approach, we consider two measures of resilience and a number of different stress models. It is shown how (i) uncertainty profiles can be ordered by risk (as measured by game valuations) and (ii) the structural properties of risk partial orders can be analysed.

We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312–316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at random with probability proportional to its assigned “fitness” value. It reproduces, placing a copy of itself on a neighbouring vertex chosen uniformly at random, replacing the individual that was there. The initial population consists of a single mutant of fitness r > 0 placed uniformly at random, with every other vertex occupied by an individual of fitness 1. The main quantities of interest are the probabilities that the descendants of the initial mutant come to occupy the whole graph (fixation) and that they die out (extinction); almost surely, these are the only possibilities. In general, exact computation of these quantities by standard Markov chain techniques requires solving a system of linear equations of size exponential in the order of the graph so is not feasible. We show that, with high probability, the number of steps needed to reach fixation or extinction is bounded by a polynomial in the number of vertices in the graph. This bound allows us to construct fully polynomial randomized approximation schemes (FPRAS) for the probability of fixation (when r ≥ 1) and of extinction (for all r > 0).

We present a model of the establishment and maintenance of communication between mobile agents. We assume that the agents move through a fixed environment modeled by a motion graph and are able to communicate if they are within distance at most d of each other. As the agents move randomly, we analyze the evolution in time of the connectivity between a set of w agents, asymptotically for a large number N of vertices, when w also grows large. The particular topologies of the environment we study here are the cycle and the toroidal grid.

Abstract In this article, we propose several variations of the adversarial queueing model and address stability issues of networks and protocols in those proposed models. The first such variation is thepriority model, which is directed at static network topologies and takes into account the case in which packets can have different priorities. Those priorities are assigned by an adversary at injection time. A second variation, thevariable priority model, is an extension of the priority model in which the adversary may dynamically change the priority of packets at each time step. Two more variations, namely thefailure modeland thereliable model, are proposed to cope with dynamic networks. In the failure and reliable models the adversary controls, under different constraints, the failures that the links of the topology might suffer. Concerning stability of networks in the proposed adversarial models, we show that the set ofuniversally stablenetworks in the adversarial model remains the same in the priority, variable priority, failure, and reliable models. From the point of view of protocols (or queueing policies), we show that several protocols that are universally stable in the adversarial queueing model remain so in the priority, failure, and reliable models. However, we show that thelongest‐in‐system(LIS) protocol, which is universally stable in the adversarial queueing model, is not universally stable in any of the other models we propose. Moreover, we show that no queueing policy is universally stable in the variable priority model. Finally, we analyze the problem of deciding stability of a given network under a fixed protocol. We provide a characterization of the networks that are stable underfirst‐in‐first‐out(FIFO) and LIS in the failure model (and therefore in the reliable and priority models). This characterization allows us to show that the stability problem under FIFO and LIS in the failure model can be solved in polynomial time. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 45(1), 23–35 2005

We study universal stability of directed and undirected graphs in the adversarial queuing model for static packet routing. In this setting, packets are injected in some edge and have to traverse a predefined path before leaving the system. Restrictions on the allowed packet trajectory provide a way to analyze stability under different packet trajectories. We consider five packet trajectories, two for directed graphs and three for undirected graphs, and provide polynomial time algorithms for testing universal stability when considering each of them. In each case we obtain a different characterization of the universal stability property in terms of a set of forbidden subgraphs. Thus we show that variations of the allowed packet trajectory lead to nonequivalent characterizations. Using those characterizations we are also able to provide polynomial time algorithms for testing stability under the \NTGLIS (Nearest To Go-Longest In System) protocol.

The main contribution of this paper is presenting a new model for Smart Dust networks communicating through optical links and showing its applicability when the goal of the network is monitoring an area under the surveillance of a base station. We analyze the basic parameters of these networks as a new model of random graphs and propose simple distributed protocols for basic communication. These protocols are designed to minimize the energy consumption.

In this paper we study the universal stability of undirected graphs in the adversarial queueing model for packet routing. In this setting, packets must be injected in some edge and have to traverse a path before leaving the system. Restrictions on the allowed types of path that packets must traverse provide different packet models. We consider three natural models, and provide polynomial time algorithms for testing universal stability on them. In the three cases, we obtain a different characterization, in terms of forbidden subgraphs, thus showing that slight variations lead to non-equivalent models.We extend those results to show that universal stability of digraphs, in the case in which packets follow directed paths without repeating vertices, can be decided in polynomial time.All the instability results are obtained for the \NTGLIS protocol. Therefore, the property of universal stability is equivalent to \NTGLIS-stability, in all the cases.

In this paper, we analyze the stability properties of the FIFO protocol in the Adversarial Queueing model for packet routing. We show a graph for which FIFO is stable for any adversary with injection rate r ≰ 0.1428. We generalize this results to show upper bound for stability of any network under FIFO protocol, answering partially an open question raised by Andrews et al. in [2]. We also design a network and an adversary for which FIFO is non-stable for any r ≱ 0.8357, improving the previous known bounds of [2].

In this paper we deal with the parallel approximability of a special class of Quadratic Programming (QP), called Smooth Positive Quadratic Programming. This subclass of QP is obtained by imposing restrictions on the coefficients of the QP instance. The Smoothness condition restricts the magnitudes of the coefficients while the positiveness requires that all the coefficients be non-negative. Interestingly, even with these restrictions several combinatorial problems can be modeled by Smooth QP. We show NC Approximation Schemes for the instances of Smooth Positive QP. This is done by reducing the instance of QP to an instance of Positive Linear Programming, finding in NC an approximate fractional solution to the obtained program, and then rounding the fractional solution to an integer approximate solution for the original problem. Then we show how to extend the result for positive instances of bounded degree to Smooth Integer Programming problems. Finally, we formulate several important combinatorial problems as Positive Quadratic Programs (or Positive Integer Programs) in packing/covering form and show that the techniques presented can be used to obtain NC Approximation Schemes for "dense" instances of such problems.

We introduce a new way of describing a subclass of CSP processes in the failures-divergence model. These processes will be called rational, by analogy with rational languages in formal language theory. Usually, rational languages are characterized as a solution of a linear system of equations. In this work we use a restricted set of CSP operators and recursion to define CSP-linear systems. We show that these systems are in many respects similar to linear systems in formal language theory. Our main result states that for linear systems the least fix point solution in a CPO can be obtained using Arden's lemma. Furthermore we give an alternative definition of the class of rational processes in terms of automata. Finally we analyze how the previous result can be extended to other semantic models.

This paper shows that the problem of testing whether a graph G contains an induced subgraph of vertex (edge) connectivity at least k is P-complete for any fixed $k \geqslant 3$. Moreover, if $k_{\max } $ is the largest vertex (edge) connectivity of any subgraph of G, it is shown that unless ${\text{P}} = {\text{NC}}$ there is no NC algorithm that approximates $k_{\max } $ within any approximation factor $\frac{1}{2} < c < 1$ (such an algorithm is by definition one that outputs a number in the interval $[ck_{\max } ,k_{\max } ]$). In contrast, it is known that the problem of finding the Tutte (triconnected) components of G (i.e., the maximal subgraphs of G such that for any four vertices in any of them, any two of these vertices can be connected by a path in G that avoids the other two) is in NC. On the positive side, it is shown, by proving extremal graph results, that the maximum k for which there is a k-edge-connected induced subgraph of G can be approximated in NC for any approximation factor strictly less than $\frac{1}{2}$ and that the same is true for vertex connectivity for any approximation factor strictly less than $\frac{1}{4}$.

It is shown that the problem of testing whether a graph G contains a vertex- (edge-) connected induced subgraph of cardinality k is P-complete for any fixed k>or=3. Moreover, it is shown that approximating within a factor c>1/2 the maximum d for which there is a d-vertex-(d-edge-) connected induced subgraph of G is not in NC, unless P=NC. In contrast, it is known that the problem of finding the Tutte (triconnected) components of G is in NC. On the positive side, it is shown by proving extremal-graph results, that the maximum d for which there is a d-edge-connected induced subgraph of G can be approximated in NC within any factor c>