Completion of the mixed unit interval graphs hierarchy

We describe the missing class of the hierarchy of mixed unit interval graphs, generated by the intersection graphs of closed, open and one type of half-open intervals of the real line. This class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic-time algorithms that recognize graphs from this class and produce a corresponding interval representation if one exists. We also mention that the work in arXiv:1405.4247 directly extends to provide a quadratic-time algorithm to recognize the class of mixed unit interval graphs.Comment: 17 pages, 36 figures (three not numbered). v1 Accepted in the TAMC 2015 conference. The recognition algorithm is faster in v2. One graph was not listed in Theorem 7 of v1 of this paper v3 provides a proposition to recognize the mixed unit interval graphs in quadratic time. v4 is a lot cleare

Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

Recent Advances in Computational Methods for the Power Flow Equations

The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and voltages in a power system. A plethora of methods have been devised to solve these equations, starting from Newton-based methods to homotopy continuation and other optimization-based methods. While many of these methods often efficiently find a high-voltage, stable solution due to its large basin of attraction, most of the methods struggle to find low-voltage solutions which play significant role in certain stability-related computations. While we do not claim to have exhausted the existing literature on all related methods, this tutorial paper introduces some of the recent advances in methods for solving power flow equations to the wider power systems community as well as bringing attention from the computational mathematics and optimization communities to the power systems problems. After briefly reviewing some of the traditional computational methods used to solve the power flow equations, we focus on three emerging methods: the numerical polynomial homotopy continuation method, Groebner basis techniques, and moment/sum-of-squares relaxations using semidefinite programming. In passing, we also emphasize the importance of an upper bound on the number of solutions of the power flow equations and review the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016 American Control Conferenc

Order-Related Problems Parameterized by Width

In the main body of this thesis, we study two different order theoretic problems. The first problem, called Completion of an Ordering, asks to extend a given finite partial order to a complete linear order while respecting some weight constraints. The second problem is an order reconfiguration problem under width constraints. While the Completion of an Ordering problem is NP-complete, we show that it lies in FPT when parameterized by the interval width of ρ. This ordering problem can be used to model several ordering problems stemming from diverse application areas, such as graph drawing, computational social choice, and computer memory management. Each application yields a special partial order ρ. We also relate the interval width of ρ to parameterizations for these problems that have been studied earlier in the context of these applications, sometimes improving on parameterized algorithms that have been developed for these parameterizations before. This approach also gives some practical sub-exponential time algorithms for ordering problems. In our second main result, we combine our parameterized approach with the paradigm of solution diversity. The idea of solution diversity is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. There, we show that the considered diversity version of the Completion of an Ordering problem is fixed-parameter tractable with respect to natural paramaters that capture the notion of diversity and the notion of sufficiently good solutions. We apply this algorithm in the study of the Kemeny Rank Aggregation class of problems, a well-studied class of problems lying in the intersection of order theory and social choice theory. Up to this point, we have been looking at problems where the goal is to find an optimal solution or a diverse set of good solutions. In the last part, we shift our focus from finding solutions to studying the solution space of a problem. There we consider the following order reconfiguration problem: Given a graph G together with linear orders τ and τ ′ of the vertices of G, can one transform τ into τ ′ by a sequence of swaps of adjacent elements in such a way that at each time step the resulting linear order has cutwidth (pathwidth) at most w? We show that this problem always has an affirmative answer when the input linear orders τ and τ ′ have cutwidth (pathwidth) at most w/2. Using this result, we establish a connection between two apparently unrelated problems: the reachability problem for two-letter string rewriting systems and the graph isomorphism problem for graphs of bounded cutwidth. This opens an avenue for the study of the famous graph isomorphism problem using techniques from term rewriting theory. In addition to the main part of this work, we present results on two unrelated problems, namely on the Steiner Tree problem and on the Intersection Non-emptiness problem from automata theory.Doktorgradsavhandlin

Rational bidding using reinforcement learning: an application in automated resource allocation

The application of autonomous agents by the provisioning and usage of computational resources is an attractive research field. Various methods and technologies in the area of artificial intelligence, statistics and economics are playing together to achieve i) autonomic resource provisioning and usage of computational resources, to invent ii) competitive bidding strategies for widely used market mechanisms and to iii) incentivize consumers and providers to use such market-based systems. The contributions of the paper are threefold. First, we present a framework for supporting consumers and providers in technical and economic preference elicitation and the generation of bids. Secondly, we introduce a consumer-side reinforcement learning bidding strategy which enables rational behavior by the generation and selection of bids. Thirdly, we evaluate and compare this bidding strategy against a truth-telling bidding strategy for two kinds of market mechanisms – one centralized and one decentralized

Behavioral synthesis from VHDL using structured modeling

This dissertation describes work in behavioral synthesis involving the development of a VHDL Synthesis System VSS which accepts a VHDL behavioral input specification and performs technology independent synthesis to generate a circuit netlist of generic components. The VHDL language is used for input and output descriptions. An intermediate representation which incorporates signal typing and component attributes simplifies compilation and facilitates design optimization.A Structured Modeling methodology has been developed to suggest standard VHDL modeling practices for synthesis. Structured modeling provides recommendations for the use of available VHDL description styles so that optimal designs will be synthesized.A design composed of generic components is synthesized from the input description through a process of Graph Compilation, Graph Criticism, and Design Compilation. Experiments were performed to demonstrate the effects of different modeling styles on the quality of the design produced by VSS. Several alternative VHDL models were examined for each benchmark, illustrating the improvements in design quality achieved when Structured Modeling guidelines were followed

A semantic-based platform for the digital analysis of architectural heritage

This essay focuses on the fields of architectural documentation and digital representation. We present a research paper concerning the development of an information system at the scale of architecture, taking into account the relationships that can be established between the representation of buildings (shape, dimension, state of conservation, hypothetical restitution) and heterogeneous information about various fields (such as the technical, the documentary or still the historical one). The proposed approach aims to organize multiple representations (and associated information) around a semantic description model with the goal of defining a system for the multi-field analysis of buildings

Higgs Dark Matter from a Warped Extra-Dimension -- the truncated-inert-doublet model

We construct a 5D $\mathbb{Z}_2$-symmetric model with three D3-branes: two IR ones with negative tension located at the ends of an extra-dimensional interval and a UV-brane with positive tension placed in the middle of the interval -- IR-UV-IR model. The background solutions for this geometric setup are found without and with taking into account the backreaction of the matter fields. A 5D $SU(2)$ Higgs doublet is employed as the Goldberger-Wise stabilizing field in this geometry and solutions of the 5D coupled scalar-gravity equations are found by using the superpotential method. Within this setup we investigate the low-energy (zero-mode) effective theory for the bulk Standard Model (SM) bosonic sector. The $\mathbb{Z}_2$-even zero-modes correspond to known standard degrees of freedom, whereas the $\mathbb{Z}_2$-odd zero modes might serve as a dark sector. The effective low-energy scalar sector contains a scalar which mimics the SM Higgs boson and a second stable scalar particle (dark-Higgs) is a dark matter candidate; the latter is a component of the zero-mode of the $\mathbb{Z}_2$-odd Higgs doublet. The model that results from the $\mathbb{Z}_2$-symmetric background geometry resembles the Inert Two Higgs Doublet Model. The effective theory turns out to have an extra residual $SU(2)\times U(1)$ global symmetry that is reminiscent of an underlying 5D gauge transformation for the odd degrees of freedom. At tree level the SM Higgs and the dark-Higgs have the same mass; however, when leading radiative corrections are taken into account the dark-Higgs turns out to be heavier than the SM Higgs. Implications for dark matter are discussed; it is found that the dark-Higgs can provide only a small fraction of the observed dark matter abundance.Comment: 38 pages, 8 figures and 2 tables. v2: a new subsection (2.2) on radius stabilization with an SU(2) bulk Higgs doublet is added, which provides exact analytic background solutions (with full backreaction) of the Higgs-gravity 5D warped setup. References added, matches the version to appear in JHE

Chordal Editing is Fixed-Parameter Tractable

Graph modification problems typically ask for a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly different versions by allowing different operations. We study a very general graph modification problem that allows all three types of operations: given a graph and integers k(1), k(2), and k(3), the CHORDAL EDITING problem asks whether G can be transformed into a chordal graph by at most k(1) vertex deletions, k(2) edge deletions, and k(3) edge additions. Clearly, this problem generalizes both CHORDAL DELETION and CHORDAL COMPLETION (also known as MINIMUM FILL-IN). Our main result is an algorithm for CHORDAL EDITING in time 2(O(klog k)). n(O(1)), where k:=k(1) + k(2) + k(3) and n is the number of vertices of G. Therefore, the problem is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm is both more efficient and conceptually simpler than the previously known algorithm for the special case CHORDAL DELETION