On the complexity of modified instances

Diese Dissertation untersucht die Komplexität modifizierter Instanzen und inwiefern sich NP-vollständige Probleme unter minimaler Veränderung stabil verhalten. Wir betrachten für verschiedene NP-vollständige Probleme, ob die Kenntnis einer Lösung einer Instanz eine Hilfe beim Entscheiden einer geringfügig modifizierten Instanz liefern kann. Außerdem untersuchen wir, inwieweit sich modifizierte Instanzen effizient entscheiden lassen, wenn nicht nur eine Lösung der unmodifizierten Instanz gegeben ist, sondern allgemeinere Hinweise, wie z.B. ein polynomiell langer String. Diese Fragestellung spielt nicht nur überall dort eine große Rolle, wo NP-vollständige Probleme in dynamischen Situationen schnell gelöst werden müssen, sondern liefert auch tiefere Einsichten in die generelle Natur der Klasse der NP-vollständigen Probleme. Des Weiteren betrachten wir das Problem der Reoptimierung. Das heißt, wir untersuchen für verschiedene Optimierungsprobleme, ob man für modifizierte Instanzen eines Optimierungsproblems eine gute Lösung finden kann, wenn bereits eine optimale Lösung einer ähnlichen Instanz bekannt ist

The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs

AbstractIn this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in “yes”-instances. For all of these problems with the exceptions of Feasible Register Assignment and Module Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W[t] for all t∈N. We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NP-Complete

Drag it together with Groupie: making RDF data authoring easy and fun for anyone

One of the foremost challenges towards realizing a “Read-write Web of Data” [3] is making it possible for everyday computer users to easily find, manipulate, create, and publish data back to the Web so that it can be made available for others to use. However, many aspects of Linked Data make authoring and manipulation difficult for “normal” (ie non-coder) end-users. First, data can be high-dimensional, having arbitrary many properties per “instance”, and interlinked to arbitrary many other instances in a many different ways. Second, collections of Linked Data tend to be vastly more heterogeneous than in typical structured databases, where instances are kept in uniform collections (e.g., database tables). Third, while highly flexible, the problem of having all structures reduced as a graph is verbosity: even simple structures can appear complex. Finally, many of the concepts involved in linked data authoring - for example, terms used to define ontologies are highly abstract and foreign to regular citizen-users.To counter this complexity we have devised a drag-and-drop direct manipulation interface that makes authoring Linked Data easy, fun, and accessible to a wide audience. Groupie allows users to author data simply by dragging blobs representing entities into other entities to compose relationships, establishing one relational link at a time. Since the underlying representation is RDF, Groupie facilitates the inclusion of references to entities and properties defined elsewhere on the Web through integration with popular Linked Data indexing services. Finally, to make it easy for new users to build upon others’ work, Groupie provides a communal space where all data sets created by users can be shared, cloned and modified, allowing individual users to help each other model complex domains thereby leveraging collective intelligence

Finding Optimal Solutions With Neighborly Help

Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal colorings for all one-edge-deleted subgraphs? Studying such questions not only gives detailed insight into the structure of the problem itself, but also into the complexity of related problems; most notably graph theory\u27s core notion of critical graphs (e.g., graphs whose chromatic number decreases under deletion of an arbitrary edge) and the complexity-theoretic notion of minimality problems (also called criticality problems, e.g., recognizing graphs that become 3-colorable when an arbitrary edge is deleted). We focus on two prototypical graph problems, Colorability and Vertex Cover. For example, we show that it is NP-hard to compute an optimal coloring for a graph from optimal colorings for all its one-vertex-deleted subgraphs, and that this remains true even when optimal solutions for all one-edge-deleted subgraphs are given. In contrast, computing an optimal coloring from all (or even just two) one-edge-added supergraphs is in P. We observe that Vertex Cover exhibits a remarkably different behavior, demonstrating the power of our model to delineate problems from each other more precisely on a structural level. Moreover, we provide a number of new complexity results for minimality and criticality problems. For example, we prove that Minimal-3-UnColorability is complete for DP (differences of NP sets), which was previously known only for the more amenable case of deleting vertices rather than edges. For Vertex Cover, we show that recognizing beta-vertex-critical graphs is complete for Theta_2^p (parallel access to NP), obtaining the first completeness result for a criticality problem for this class

Scheduling Independent Moldable Tasks on Multi-Cores with GPUs

The number of parallel systems using accelerators is growing up.The technology is now mature enough to allow sustainedpetaflop/s. However, reaching this performance scale requiresefficient scheduling algorithms to manage the heterogeneouscomputing resources.We present a new approach for scheduling independent tasks onmultiple CPUs and multiple GPUs. The tasks are assumed to beparallelizable on CPUs using the moldable model: the final numberof cores allotted to a task can be decided and set by thescheduler. More precisely, we design an algorithm aiming atminimizing the makespan---the maximum completion time of alltasks---for this scheduling problem. The proposed algorithmcombines a dual approximation scheme with a fast integer linearprogram (ILP). It determines both the partitioning of the tasks,ie whether a task should be mapped to CPUs or a GPU, and thenumber of CPUs allotted to a moldable task if mapped to the CPUs.A worst case analysis shows that the algorithm has anapproximation ratio of $\frac{3}{2} + \epsilon$. However, sincethe complexity of the ILP-based algorithm could benon-polynomial, we also present a proved polynomial-timealgorithm with an approximation ratio of $2+\epsilon$.We complement the theoretical analysis of our two novelalgorithms with an experimental study. In these experiments, wecompare our algorithms to a modified version of the classical\heft algorithm, adapted to handle moldable tasks. Theexperimental results show that our algorithm with the$\frac{3}{2} + \epsilon$ approximation ratio producessignificantly shorter schedules than the modified \heft for mostof the instances. In addition, the experiments provide evidencethat this ILP-based algorithm is also practically able to solvelarger problem instances in a reasonable amount of time