Ulrike Stege

Solving large FPT problems on coarse-grained parallel machines

Fixed-parameter tractability (FPT) techniques have recently been successful in solving NP-complete problem instances of practical importance which were too large to be solved with previous methods. In this paper, we show how to enhance this approach through the addition of parallelism, thereby allowing even larger problem instances to be solved in practice. More precisely, we demonstrate the potential of parallelism when applied to the bounded-tree search phase of FPT algorithms. We apply our methodology to the k-VERTEX COVER problem which has important applications in, for example, the analysis of multiple sequence alignments for computational biochemistry. We have implemented our parallel FPT method for the k-VERTEX COVER problem using C and the MPI communication library, and tested it on a 32-node Beowulf cluster. This is the first experimental examination of parallel FPT techniques. As part of our experiments, we solved larger instances of k-VERTEX COVER than in any previously reported implementations. For example, our code can solve problem instances with k≥400 in less than 1.5 h.

Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems

Abstract We obtain faster algorithms for problems such as r-dimensional matching and r-set packing when the size k of the solution is considered a parameter. We first establish a general framework for finding and exploiting small problem kernels (of size polynomial in k). This technique lets us combine Alon, Yuster and Zwick’s color-coding technique with dynamic programming to obtain faster fixed-parameter algorithms for these problems. Our algorithms run in time O(n+2O(k)), an improvement over previous algorithms for some of these problems running in time O(n+kO(k)). The flexibility of our approach allows tuning of algorithms to obtain smaller constants in the exponent.

Coordinatized Kernels and Catalytic Reductions: An Improved FPT Algorithm for Max Leaf Spanning Tree and Other Problems

We describe some new, simple and apparently general methods for designing FPT algorithms, and illustrate how these can be used to obtain a significantly improved FPT algorithm for the MAXIMUM LEAF SPANNING TREE problem. Furthermore, we sketch how the methods can be applied to a number of other well-known problems, including the parametric dual of DOMINATING SET (also known as NONBLOCKER), MATRIX DOMINATION, EDGE DOMINATING SET, and FEEDBACK VERTEX SET FOR UNDIRECTED GRAPHS. The main payoffs of these new methods are in improved functions f(k) in the FPT running times, and in general systematic approaches that seem to apply to a wide variety of problems.

Convex hull and tour crossings in the Euclidean traveling salesperson problem: Implications for human performance studies

Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull hypothesis, originally proposed by MacGregor and Ormerod (1996). We argue that, in the literature so far, there is no evidence for this hypothesis. Alternatively we propose and motivate the hypothesis that people aim at avoiding crossings.

Refined Search Tree Technique for DOMINATING SET on Planar Graphs

We establish refined search tree techniques for the parameterized dominating set problem on planar graphs. We derive a fixed parameter algorithm with running time O(8kn), where k is the size of the dominating set and n is the number of vertices in the graph. For our search tree, we firstly provide a set of reduction rules. Secondly, we prove an intricate branching theorem based on the Euler formula. In addition, we give an example graph showing that the bound of the branching theorem is optimal with respect to our reduction rules. Our final algorithm is very easy (to implement); its analysis, however, is involved.

Gene Trees and Species Trees: The Gene-Duplication Problem in Fixed-Parameter Tractable

GENE DUPLICATION is the problem of computing an optimal species tree for a given set of gene trees under the GENE DUPLICATION Model (first introduced by Goodman et al.). The problem is known to be NP-complete. We give a fixed-parameter-tractable algorithm solving the problem parameterized by the number of gene duplications necessary to rectify the gene trees with respect to the species tree.

On the Multiple Gene Duplication Problem

A fundamental problem in computational biology is the determination of the correct species tree for a set of taxa given a set of (possibly contradictory) gene trees. In recent literature, the DUPLICATION/ LOSS model has received considerable attention. Here one measures the similarity/dissimilarity between a set of gene trees by counting the number of paralogous gene duplications and subsequent gene losses which need to be postulated in order to explain (in an evolutionarily meaningful way) how the gene trees could have arisen with respect to the species tree. Here we count the number of multiple gene duplication events (duplication events in the genome of the organism involving one or more genes) without regard to gene losses. MULTIPLE GENE DUPLICATION asks to find the species tree S which requires the fewest number of multiple gene duplication events to be postulated in order to explain a set of gene trees G1, G2,..., Gk. We also examine the related problem which assumes the species tree S is known and asks to find the explanation for G1, G2,..., Gk requiring the fewest multiple gene duplications. Via a reduction to and from a combinatorial model we call the BALL AND TRAP GAME, we show that the general form of this problem is NP-hard and various parameterized versions are hard for the complexity class W[1]. These results immediately imply that MULTIPLE GENE DUPLICATION is similarily hard. We prove that several parameterized variants are in FPT.

Information Brokers in Requirement-Dependency Social Networks

Requirements interdependencies create technical dependencies among project members that generally belong to different functional groups in an organization, but who need to coordinate activities during processes of requirements change management. Effective knowledge management is needed to disseminate information on requirement changes across teams working on interdependent requirements to avoid mis-interpretations. Social networks are regarded as important in fostering knowledge management, where brokers or gatekeepers have the role of project members facilitating information flow. However, little is known about processes of information flow and brokerage in social networks built around interdependent requirements. In a field study of requirement interdependencies in a large IT manufacturing organization, we found that brokers holding pockets of knowledge have an impact on information flow in requirement-interdependent teams. We discuss a number of patterns of information flow and draw implications for processes of requirements change management.

A new method for indexing genomes using on-disk suffix trees

We propose a new method to build persistent suffix trees for indexing the genomic data. Our algorithm DiGeST (Disk-Based Genomic Suffix Tree) improves significantly over previous work in reducing the random access to the input string and performing only two passes over disk data. DiGeST is based on the two-phase multi-way merge sort paradigm using a concise binary representation of the DNA alphabet. Furthermore, our method scales to larger genomic data than managed before.

Autonomic Computing Now You See It, Now You Don't

With the rapid growth of web services and socio-technical ecosystems, the management complexity of these modern, decentralized, distributed computing systems presents significant challenges for businesses and often exceeds the capabilities of human operators. Autonomic computing is an effective set of technologies, models, architecture patterns, standards, and processes to cope with and reign in the management complexity of dynamic computing systems using feedback control, adaptation, and self-management. At the core of an autonomic system are control loops which sense their environment, model their behavior in that environment, and take action to change the environment or their own behavior. Computer science researchers often approach the design of such highly dynamical systems from a software architecture perspective whereas engineering researchers start with a feedback control perspective. In this article, we argue that both design perspectives are needed and necessary for autonomic system design.