On the Parameterized Complexity of the Maximum Edge 2-Coloring Problem

We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q >= 2 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q >= 2, and has been well-studied from the point of view of approximation. Our main focus is the case when q = 2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel.

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs

We address the parameterized complexity ofMaxColorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril IPL 1987] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n(O(q)) algorithm on chordal graphs. We first observe that the problem is W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q >= 2.

The undirected feedback vertex set problem has a Poly(k) Kernel

Resolving a noted open problem, we show that the Undirected Feedback Vertex Set problem, parameterized by the size of the solution set of vertices, is in the parameterized complexity class Poly(k), that is, polynomial-time pre-processing is sufficient to reduce an initial problem instance (G, k) to a decision-equivalent simplified instance (G', k') where k' � k, and the number of vertices of G' is bounded by a polynomial function of k. Our main result shows an O(k11) kernelization bound.

Treewidth: theory and applications to computer science

This report is an introduction to the concept of treewidth, a property of graphs that has important implications in algorithms. Some basic concepts of graph theory are presented in the first chapter for those readers that are not familiar with the notation. In Chapter 2, the definition of treewidth and some different ways of characterizing it are explained. The last two chapters focus on the algorithmic implications of treewidth, which are very relevant in Computer Science. An algorithm to compute the treewidth of a graph is presented and its result can be later applied to many other problems in graph theory, like those introduced in the last chapter.

Tipos de lógica utilizadas en la toma de decisiones estratégicas de marketing

Para el administrador el proceso de la toma de decisiones es uno de sus mayores retos y responsabilidades, ya que en su desarrollo se debe definir el camino más acertado en un sin número de alternativas, teniendo en cuenta los obstáculos sociales, políticos y económicos del entorno empresarial. Para llegar a la decisión adecuada no hay que perder de vista los objetivos y metas propuestas, además de tener presente el proceso lógico, detectando, analizando y demostrando el porqué de esa elección. Consecuentemente el análisis que propone esta investigación aportara conocimientos sobre los tipos de lógica utilizados en la toma de decisiones estratégicas al administrador para satisfacer las demandas asociadas con el mercadeo para que de esta manera se pueda generar y ampliar eficientemente las competencia idóneas del administrador en la inserción internacional de un mercado laboral cada vez mayor (Valero, 2011). A lo largo de la investigación se pretende desarrollar un estudio teórico para explicar la relación entre la lógica y la toma de decisiones estratégicas de marketing y como estos conceptos se combinan para llegar a un resultado final. Esto se llevara a cabo por medio de un análisis de planes de marketing, iniciando por conceptos básicos como marketing, lógica, decisiones estratégicas, dirección de marketing seguido de los principios lógicos y contradicciones que se pueden llegar a generar entre la fundamentación teórica

Parameterized Algorithms and Kernels for 3-Hitting Set with Parity Constraints

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U. The goal is to find a subset of U of the smallest possible size that intersects every set in F. The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the intersections of S with each set in the family F. In particular, an odd (even) set is a hitting set that hits every set at either one or three (two) elements, and a perfect code is a hitting set that intersects every set at exactly one element. These questions are of fundamental interest in many contexts for general set systems. Just as for Hitting Set, we find these questions to be interesting for the case of families consisting of sets of size at most three. In this work, we initiate an algorithmic study of these problems in this special case, focusing on a parameterized analysis. We show, for each problem, efficient fixed-parameter tractable algorithms using search trees that are tailor-made to the constraints in question, and also polynomial kernels using sunflower-like arguments in a manner that accounts for equivalence under the additional parity constraints.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Low-complexity estimation of CFO and frequency independent I/Q mismatch for OFDM systems

CFO and I/Q mismatch could cause significant performance degradation to OFDM systems. Their estimation and compensation are generally difficult as they are entangled in the received signal. In this paper, we propose some low-complexity estimation and compensation schemes in the receiver, which are robust to various CFO and I/Q mismatch values although the performance is slightly degraded for very small CFO. These schemes consist of three steps: forming a cosine estimator free of I/Q mismatch interference, estimating I/Q mismatch using the estimated cosine value, and forming a sine estimator using samples after I/Q mismatch compensation. These estimators are based on the perception that an estimate of cosine serves much better as the basis for I/Q mismatch estimation than the estimate of CFO derived from the cosine function. Simulation results show that the proposed schemes can improve system performance significantly, and they are robust to CFO and I/Q mismatch.

How environmental and organizational complexity affects opportunity recognition in development projects

New product development projects are experiencing increasing internal and external project complexity. Complexity leadership theory proposes that external complexity requires adaptive and enabling leadership, which facilitates opportunity recognition (OR). We ask whether internal complexity also requires OR for increased adaptability. We extend a model of EO and OR to conclude that internal complexity may require more careful OR. This means that leaders of technically or structurally complex projects need to evaluate opportunities more carefully than those in projects with external or technological complexity.

A model of project complexity : distinguishing dimensions of complexity from severity

There is increasing agreement that understanding complexity is important for project management because of difficulties associated with decision-making and goal attainment which appear to stem from complexity. However the current operational definitions of complex projects, based upon size and budget, have been challenged and questions have been raised about how complexity can be measured in a robust manner that takes account of structural, dynamic and interaction elements. Thematic analysis of data from 25 in-depth interviews of project managers involved with complex projects, together with an exploration of the literature reveals a wide range of factors that may contribute to project complexity. We argue that these factors contributing to project complexity may define in terms of dimensions, or source characteristics, which are in turn subject to a range of severity factors. In addition to investigating definitions and models of complexity from the literature and in the field, this study also explores the problematic issues of ‘measuring’ or assessing complexity. A research agenda is proposed to further the investigation of phenomena reported in this initial study.